problem solving with powers of 10

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Powers of 10

Here you will learn about powers of 10, including what they are and how to write and solve equations using powers of 10.

Students will first learn about powers of 10 as part of numbers and operations in base ten in 5th grade.

What are powers of 10?

Powers of \bf{10} are 10 multiplied by itself over and over again and written with exponents.

For example,

Since our number system is Base 10 (meaning each place value position is grouped by tens), when numbers are multiplied or divided by powers of 10, place value patterns are created.

\begin{aligned} & 67 \times 10=670 \\\\ & 67 \times 10^2=6,700 \\\\ & 67 \times 10^3=67,000 \end{aligned}

The digits from the original number (67) are always in the product, but they increase in place value.

Notice that each time an additional 10 is multiplied, the number of place value positions the digits move increases by one.

This is also true when dividing with powers of 10.

\begin{aligned} & 67 \div 10=6.7 \\\\ & 67 \div 10^2=0.67 \\\\ & 67 \div 10^3=0.067 \end{aligned}

The digits for the original number (67) are always in the quotient, but they decrease in place value.

Notice that each time an additional 10 is divided, the number of places the digits move increases by one.

Common Core State Standards

How does this relate to 5th and 6th grade math?

• Grade 5 – Numbers and Operations in Base Ten (5.NBT.2) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number powers of 10 to denote powers of 10.

How to use powers of 10

In order to represent a number as a power of 10 :

Show the number as an expression with multipliers of \bf{10} .

Count the number of \bf{10} s in the expression to create the power of \bf{10} .

Write the equation.

In order to solve an expression with a power of 10 :

Use place value reasoning to identify how the power of \bf{10} will change the number.

Shift the digits left if multiplying and shift the digits right if dividing.

[FREE] Exponents Check for Understanding Quiz (Grade 4 to 6)

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Powers of 10 examples

Example 1: number as a power of 10.

Write 45,000 as a power of 10.

45,000 is the same as 45 thousands or 45 \times 1,000.

1,000 as a product of tens is 10 \times 10 \times 10, so…

45,000=45 \times 10 \times 10 \times 10

2 Count the number of \bf{10} s in the expression to create the power of \bf{10} .

There are 3 tens being multiplied. Use 10 as the base and 3 as the exponent.

3 Write the equation.

45,000=45 \times 10^3

*Note: You can show 45,000 with other powers of 10. See how in the next example.

Example 2: number as multiple powers of 10

Write 1,030,000 as two different powers of 10.

1,030,000 is the same as 103 ten-thousands or 103 \times 10,000.

10,000 as a product of tens is 10 \times 10 \times 10 \times 10, so…

1,030,000=103 \times 10 \times 10 \times 10 \times 10

1,030,000 is also the same as 1,030 thousands or 1,030 \times 1,000.

1,030,000=1,030 \times 10 \times 10 \times 10

There are 4 tens being multiplied. Use 10 as the base and 4 as the exponent.

1,030,000=103 \times 10^4

1,030,000=1,030 \times 10^3

*Note: The example shows two possible powers of 10 equations, but any place value can be used to show powers of 10.

Example 3: expression with a power of 10 – product

Solve 5.3 \times 10^6 using place value reasoning.

10^6=10 \times 10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times larger than the position to the right, 5.3 will be 6 place value positions larger after it is multiplied by 10^6.

Multiplying by 10, makes a number 10 times larger, which shifts the digits to the left.

For \times 10^6, shift the digits 6 positions to the left.

Example 4: expression with a power of 10 – quotient

Solve 80,800,000 \div 10^7 using place value reasoning.

10^7=10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 80,800,000 will be 7 place value positions smaller after it is divided by 10^7.

Dividing by 10, makes a number 10 times smaller, shifts the digits to the right.

For \div 10^7, shift the digits 7 positions to the right.

Example 5: expression with a power of 10 – missing operation and power of 10

Complete the equation using an operation with a power of 10 :

The 5 in 5.16 is in the ones position.

The 5 in 51,600 is in the ten-thousands position.

From 5.16 to 51,600 the power of 10 changes the number by 4 place value positions.

This means the power of 10 is 10^4.

The place value of the 5, 1 , and 6 grows larger by 4 positions. Because of this, the digits shift to the left and the operation is multiplication.

5.16 \times 10^4=51,600

Example 6: expression with a power of 10 – missing dividend

Complete the equation:

10^8=10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 0.109 is 8 place value positions smaller than the dividend that was divided by 10^8.

The 1, 0 , and 9 in dividend will be 8 place value positions larger than in the quotient, 0.109.

Even though the equation operation is division, to find the quotient, work backwards and shift the digits to the left.

10,900,000 \div 10^8=0.109

Teaching tips for powers of 10

• Throughout teaching this skill, never forget that the main purpose is for students to explain patterns and deepen their understanding of place value. While the rules “moving the decimal point” or “adding zeros” may come up in discussions, students who memorize these rules and never make place value connections will not truly master the standard – even if they can rotely solve these types of problems.
• Worksheets are useful for this skill, but be sure they include a variety of question types. Worksheets that only include solving for the product or quotient and/or do not ask students to explain the place value connection, will promote only a rote understanding of this skill.

Easy mistakes to make

• Not knowing what to do when there are \bf{0} s within (not just at the end) Students are quick to notice a pattern between the power of 10 and the amount of 0 s at the end of many numbers. However, if students only see numbers that have 0 s at the end, they may create solving strategies that don’t work with all numbers. This could cause mistakes when dealing with numbers like 304,000 or expressions like 5.06 \times 10^4. It is important to expose students to these types of numbers and equations from the beginning, to help avoid this misconception.

• Forgetting about an exponent of \bf{1} 10 by itself is technically 10^1. It is not typically written this way, but it is important to remember that the exponent of 1 is there.

Related exponents lessons

• Negative exponents

Practice powers of 10 questions

1. Which expression shows 19,000 as a power of 10?

19,000 is the same as 19 thousands or 19 \times 1,000.

19,000=19 \times 10 \times 10 \times 10

19,000=19 \times 10^3

2. Which expression shows 2,030,000 as a power of 10?

2,300,000 is the same as 2.03 millions or 2.03 \times 1,000,000.

1,000,000 as a product of tens is 10 \times 10 \times 10 \times 10 \times 10 \times 10, so…

2,030,000=2.03 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10

There are 6 tens being multiplied. Use 10 as the base and 6 as the exponent.

2,030,000=2.03 \times 10^6

3. Solve 180 \times 10^5.

10^5=10 \times 10 \times 10 \times 10 \times 10

Since each place value is 10 times larger than the position to the right, 180 will be 5 place value positions larger after it is multiplied by 10^5.

Multiplying by 10, moves all the digits up one position.

For \times 10^5, shift the digits 5 times to the left.

Notice in this case, since 180 is a whole number, that \times 10^5 also “adds” 5 zeros.

This happens for the same reason the decimal point “moves.”

The place value is growing by 5 positions, so each new position needs a 0 as a place holder.

4. Solve 4,100 \div 10^4.

10^4=10 \times 10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 4,100 will be 4 place value positions smaller after it is divided by 10^4.

Dividing by 10, shifts all the digits down one position.

For \div 10^4, shift the digits 4 times to the right.

5. Which equation is true?

The 4 in 4.6 is in the ones position.

The 4 in 460,000,000 is in the hundred-millions position.

This is a change of 8 place value positions.

This means the power of 10 is 10^8.

The place value of the 4 and 6 grows larger by 8 positions. Because of this, the digits shift to the left and the operation is multiplication.

6. Which number completes the equation?

10^3=10 \times 10 \times 10

Since each place value is 10 times smaller than the position to the left, 702 is 3 place value positions smaller than the dividend that was divided by 10^3.

The 7, 0 , and 2 in dividend will be 3 place value positions larger than in the quotient, 702.

702,000 \div 10^3 = 702

Powers of 10 FAQs

For this standard, powers of 10 are useful in identifying and understanding place value patterns. In later grades, this skill is referred to as scientific notation and is used to represent very small numbers and very large numbers in a more efficient way.

The number of times the decimal place moves is the same as the exponent when 10 is the base. The operation, multiplication or division, tells which direction to move the decimal place.

Yes, although this standard only covers positive powers, in later grades, students will work with negative powers of ten.

Per the Common Core, in 5th grade, students work with the tenth, hundredth, and thousandth positions. However, in real world applications, powers of 10 have no limit as to how many decimal points they can represent. It is common that they include numbers up to billionth or even smaller positions. In fact, one of the purposes of powers of 10 is to make it easier to write very, very small numbers.

Yes, scientific calculators in particular include an exponent function that can be used to input and solve an equation with a power of 10.

The next lessons are

• Algebraic expressions
• Math equations
• Inequalities

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Powers of Ten Worksheets

Welcome to the powers of ten math worksheets page at Math-Drills.com where you have the power to learn this important skill! This page includes Powers of ten math worksheets with whole numbers and decimals in comma/point and point/comma formats for students to learn this important skill.

Understanding how to multiply and divide by powers of ten is one of those essential skills that students can't do without. It makes it easier to use estimation skills, it is essential in learning large and small numbers, and solidifies an understanding of place value and numbers in general. This page includes a lot of powers of ten worksheets with whole numbers on them because there are fewer digits to work with and the decimal place is in a consistent location which means that the whole number worksheets will prove to be a nice stepping stone to the more difficult decimal versions further down the page.

Positive powers of ten refers to 10, 100, and 1,000. Negative powers of ten refers to 0.1, 0.01, and 0.001. We've supplied worksheets in both standard form and exponent form. In case this is new to you, 10 -3 = 0.001, 10 -2 = 0.01, 10 -1 = 0.1, 10 0 = 1, 10 1 = 10, 10 2 = 100, 10 3 = 1000.

Most Popular Powers of Ten Worksheets this Week

Learning Powers of Ten

The learning to multiply by powers of ten worksheets include the same number multiplied by the positive or negative powers of ten. This allows students to see patterns in multiplying or dividing by a set of powers of ten.

A good place to start is with the powers of ten in standard form. Later on, introduce students to the exponent form as they will already know how to multiply or divide with powers of ten and can focus on learning the relationship between the exponents and the number of zeros they need to work with.

• Learning To Multiply Whole Numbers By Powers Of Ten (Standard Form) Numbers from 1 to 10 × Positive Powers of Ten (Standard Form) Two-Digit Numbers × Positive Powers of Ten (Standard Form) Numbers from 1 to 10 × Negative Powers of Ten (Standard Form) Two-Digit Numbers × Negative Powers of Ten (Standard Form) Whole Number × Negative Powers of Ten (Whole Number Results) (Standard Form)
• Learning To Multiply Whole Numbers By Powers Of Ten (Exponent Form) Numbers from 1 to 10 × Positive Powers of Ten ( Exponent Form) Two-Digit Numbers × Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Negative Powers of Ten ( Exponent Form) Two-Digit Numbers × Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Negative Powers of Ten (Whole Number Results) ( Exponent Form)

Multiplying with multiples of powers of ten has tremendous benefits in mental math. Think about long multiplication which is essentially multiplying by multiples of powers of ten. For example, 456 × 4 can be thought of as 4 × 400 + 4 × 50 + 4 × 6. The more comfortable students are with handling all those extra zeros, the less often they will make mistakes.

• Learning To Multiply Whole Numbers By Multiples of Powers Of Ten (Standard Form) Numbers from 1 to 10 × Multiples of Positive Powers of Ten (Standard Form) Two-Digit Numbers × Multiples of Positive Powers of Ten (Standard Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Standard Form) Two-Digit Numbers × Multiples of Negative Powers of Ten (Standard Form) Whole Number × Multiples of Negative Powers of Ten (Whole Number Results) (Standard Form)
• Learning To Multiply Whole Numbers By Multiples of Powers Of Ten (Exponent Form) Numbers from 1 to 10 × Multiples of Positive Powers of Ten ( Exponent Form) Two-Digit Numbers × Multiples of Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten ( Exponent Form) Two-Digit Numbers × Multiples of Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Whole Number Results) ( Exponent Form)

The learning to divide by powers of ten worksheets include the same number divided by the positive or negative powers of ten.

• Learning To Divide Whole Numbers By Powers Of Ten (Standard Form) Numbers from 1 to 10 ÷ Positive Powers of Ten (Standard Form) Two-Digit Numbers ÷ Positive Powers of Ten (Standard Form) Numbers from 1 to 10 ÷ Negative Powers of Ten (Standard Form) Two-Digit Numbers ÷ Negative Powers of Ten (Standard Form) Whole Number ÷ Positive Powers of Ten (Whole Number Results)
• Learning To Divide Whole Numbers By Powers Of Ten (Exponent Form) Numbers from 1 to 10 ÷ Positive Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Negative Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Positive Powers of Ten (Whole Number Results) ( Exponent Form)
• Learning To Divide Whole Numbers By Multiples of Powers Of Ten (Standard Form) Numbers ÷ Multiples of Positive Powers of Ten (Standard Form) (Quotients 1 to 10 ) Numbers ÷ Multiples of Positive Powers of Ten (Standard Form) (Quotients 10 to 99 ) Numbers ÷ Multiples of Negative Powers of Ten (Standard Form) (Quotients 1 to 10 ) Numbers ÷ Multiples of Negative Powers of Ten (Standard Form) (Quotients 10 to 99 ) Whole Number ÷ Multiples of Positive Powers of Ten (Whole Number Results)
• Learning To Divide Whole Numbers By Multiples of Powers Of Ten (Exponent Form) Numbers from 1 to 10 ÷ Multiples of Positive Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Multiples of Positive Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Multiples of Negative Powers of Ten ( Exponent Form) Two-Digit Numbers ÷ Multiples of Negative Powers of Ten ( Exponent Form) Numbers from 1 to 10 ÷ Multiples of Positive Powers of Ten (Whole Number Results) ( Exponent Form)

Multiplying and Dividing Whole Numbers by Powers of Ten

Multiplying by positive powers of ten always makes a number larger in absolute value. Conversely, multiplying by negative powers of ten always makes a number smaller in absolute value. Multiplying by 10 0 is the same as multiplying by 1.

• Multiplying Whole Numbers By Powers Of Ten (Standard Form) Whole Number × All Powers of Ten (Standard Form) Whole Number × All Positive Powers of Ten (Standard Form) Whole Number × All Negative Powers of Ten (Standard Form) Whole Number × 0.001 Whole Number × 0.01 Whole Number × 0.1 Whole Number × 10 Whole Number × 100 Whole Number × 1,000
• Multiplying Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × All Powers of Ten (Exponent Form) Whole Number × All Positive Powers of Ten (Exponent Form) Whole Number × All Negative Powers of Ten (Exponent Form) Whole Number × 10 -3 Whole Number × 10 -2 Whole Number × 10 -1 Whole Number × 10 1 Whole Number × 10 2 Whole Number × 10 3
• European Format Multiplying Whole Numbers By Powers Of Ten (Standard Form) Whole Number × All Powers of Ten (Standard Form) Whole Number × All Positive Powers of Ten (Standard Form) Whole Number × All Negative Powers of Ten (Standard Form) Whole Number × 0,001 Whole Number × 0,01 Whole Number × 0,1 Whole Number × 10 Whole Number × 100 Whole Number × 1.000
• European Format Multiplying Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × All Powers of Ten (Exponent Form) Whole Number × All Positive Powers of Ten (Exponent Form) Whole Number × All Negative Powers of Ten (Exponent Form) Whole Number × 10 -3 Whole Number × 10 -2 Whole Number × 10 -1 Whole Number × 10 1 Whole Number × 10 2 Whole Number × 10 3

Dividing by positive powers of ten always makes a number smaller in absolute value. Conversely, dividing by negative powers of ten always makes a number larger in absolute value. Dividing by 10 0 is the same as dividing by 1.

• Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number ÷ All Powers of Ten (Standard Form) Whole Number ÷ All Positive Powers of Ten (Standard Form) Whole Number ÷ All Negative Powers of Ten (Standard Form) Whole Number ÷ 0.001 Whole Number ÷ 0.01 Whole Number ÷ 0.1 Whole Number ÷ 10 Whole Number ÷ 100 Whole Number ÷ 1,000
• Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number ÷ All Powers of Ten (Exponent Form) Whole Number ÷ All Positive Powers of Ten (Exponent Form) Whole Number ÷ All Negative Powers of Ten (Exponent Form) Whole Number ÷ 10 -3 Whole Number ÷ 10 -2 Whole Number ÷ 10 -1 Whole Number ÷ 10 1 Whole Number ÷ 10 2 Whole Number ÷ 10 3
• European Format Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number : All Powers of Ten (Standard Form) Whole Number : All Positive Powers of Ten (Standard Form) Whole Number : All Negative Powers of Ten (Standard Form) Whole Number : 0,001 Whole Number : 0,01 Whole Number : 0,1 Whole Number : 10 Whole Number : 100 Whole Number : 1.000
• European Format Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number : All Powers of Ten (Exponent Form) Whole Number : All Positive Powers of Ten (Exponent Form) Whole Number : All Negative Powers of Ten (Exponent Form) Whole Number : 10 -3 Whole Number : 10 -2 Whole Number : 10 -1 Whole Number : 10 1 Whole Number : 10 2 Whole Number : 10 3

These math worksheets should help to mix things up a bit. Mixing up operations on a page helps students pay attention to detail and challenges them to access more processes while they complete the questions. The first worksheets below include all of the powers of ten from 0.001 to 1,000.

• Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number × or ÷ All Powers of Ten (Standard Form) Whole Number × or ÷ All Positive Powers of Ten (Standard Form) Whole Number × or ÷ All Negative Powers of Ten (Standard Form) Whole Number × or ÷ 0.001 Whole Number × or ÷ 0.01 Whole Number × or ÷ 0.1 Whole Number × or ÷ 10 Whole Number × or ÷ 100 Whole Number × or ÷ 1,000
• Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × or ÷ All Powers of Ten (Exponent Form) Whole Number × or ÷ All Positive Powers of Ten (Exponent Form) Whole Number × or ÷ All Negative Powers of Ten (Exponent Form) Whole Number × or ÷ 10 -3 Whole Number × or ÷ 10 -2 Whole Number × or ÷ 10 -1 Whole Number × or ÷ 10 1 Whole Number × or ÷ 10 2 Whole Number × or ÷ 10 3
• European Format Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Standard Form) Whole Number × or : All Powers of Ten (Standard Form) Whole Number × or : All Positive Powers of Ten (Standard Form) Whole Number × or : All Negative Powers of Ten (Standard Form) Whole Number × or : 0,001 Whole Number × or : 0,01 Whole Number × or : 0,1 Whole Number × or : 10 Whole Number × or : 100 Whole Number × or : 1.000
• European Format Mixed Multiplying/Dividing Whole Numbers By Powers Of Ten (Exponent Form) Whole Number × or : All Powers of Ten (Exponent Form) Whole Number × or : All Positive Powers of Ten (Exponent Form) Whole Number × or : All Negative Powers of Ten (Exponent Form) Whole Number × or : 10 -3 Whole Number × or : 10 -2 Whole Number × or : 10 -1 Whole Number × or : 10 1 Whole Number × or : 10 2 Whole Number × or : 10 3

Multiplying and Dividing Decimals by Powers of Ten

Unlike the whole number worksheets above, these worksheets and the dividing and mixed versions that follow include more digits, more need to know place value and consequently, more of a challenge. This is probably not a good place to start if your students are just learning how to multiply and divide by powers of ten. Instead, try the whole number worksheets further up the page. If they are ready, these worksheets should prove to be a fine challenge and will go a long way in helping your students to be successful in their mathematics learning.

• Multiplying Decimal Numbers By Powers Of Ten (Standard Form) Decimal × All Powers of Ten (Standard Form) Decimal × All Positive Powers of Ten (Standard Form) Decimal × All Negative Powers of Ten (Standard Form) Decimal × 0.001 Decimal × 0.01 Decimal × 0.1 Decimal × 10 Decimal × 100 Decimal × 1,000
• Multiplying Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × All Powers of Ten (Exponent Form) Decimal × All Positive Powers of Ten (Exponent Form) Decimal × All Negative Powers of Ten (Exponent Form) Decimal × 10 -3 Decimal × 10 -2 Decimal × 10 -1 Decimal × 10 1 Decimal × 10 2 Decimal × 10 3
• European Format Multiplying Decimal Numbers By Powers Of Ten (Standard Form) Decimal × All Powers of Ten (Standard Form) Decimal × All Positive Powers of Ten (Standard Form) Decimal × All Negative Powers of Ten (Standard Form) Decimal × 0,001 Decimal × 0,01 Decimal × 0,1 Decimal × 10 Decimal × 100 Decimal × 1.000
• European Format Multiplying Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × All Powers of Ten (Exponent Form) Decimal × All Positive Powers of Ten (Exponent Form) Decimal × All Negative Powers of Ten (Exponent Form) Decimal × 10 -3 Decimal × 10 -2 Decimal × 10 -1 Decimal × 10 1 Decimal × 10 2 Decimal × 10 3

It sometimes takes a little time for students to wrap their heads around dividing by powers of ten, especially by negative powers of ten. This is because students are usually taught that dividing makes a number smaller, but when dividing by negative powers of ten, the result is a larger number. Of course, this only applies to numbers that were positive to begin with....

• Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal ÷ All Powers of Ten (Standard Form) Decimal ÷ All Positive Powers of Ten (Standard Form) Decimal ÷ All Negative Powers of Ten (Standard Form) Decimal ÷ 0.001 Decimal ÷ 0.01 Decimal ÷ 0.1 Decimal ÷ 10 Decimal ÷ 100 Decimal ÷ 1,000
• Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal ÷ All Powers of Ten (Exponent Form) Decimal ÷ All Positive Powers of Ten (Exponent Form) Decimal ÷ All Negative Powers of Ten (Exponent Form) Decimal ÷ 10 -3 Decimal ÷ 10 -2 Decimal ÷ 10 -1 Decimal ÷ 10 1 Decimal ÷ 10 2 Decimal ÷ 10 3
• European Format Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal : All Powers of Ten (Standard Form) Decimal : All Positive Powers of Ten (Standard Form) Decimal : All Negative Powers of Ten (Standard Form) Decimal : 0,001 Decimal : 0,01 Decimal : 0,1 Decimal : 10 Decimal : 100 Decimal : 1.000
• European Format Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal : All Powers of Ten (Exponent Form) Decimal : All Positive Powers of Ten (Exponent Form) Decimal : All Negative Powers of Ten (Exponent Form) Decimal : 10 -3 Decimal : 10 -2 Decimal : 10 -1 Decimal : 10 1 Decimal : 10 2 Decimal : 10 3
• Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal × or ÷ All Powers of Ten (Standard Form) Decimal × or ÷ All Positive Powers of Ten (Standard Form) Decimal × or ÷ All Negative Powers of Ten (Standard Form) Decimal × or ÷ 0.001 Decimal × or ÷ 0.01 Decimal × or ÷ 0.1 Decimal × or ÷ 10 Decimal × or ÷ 100 Decimal × or ÷ 1,000
• Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × or ÷ All Powers of Ten (Exponent Form) Decimal × or ÷ All Positive Powers of Ten (Exponent Form) Decimal × or ÷ All Negative Powers of Ten (Exponent Form) Decimal × or ÷ 10 -3 Decimal × or ÷ 10 -2 Decimal × or ÷ 10 -1 Decimal × or ÷ 10 1 Decimal × or ÷ 10 2 Decimal × or ÷ 10 3
• European Format Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Standard Form) Decimal × or : All Powers of Ten (Standard Form) Decimal × or : All Positive Powers of Ten (Standard Form) Decimal × or : All Negative Powers of Ten (Standard Form) Decimal × or : 0,001 Decimal × or : 0,01 Decimal × or : 0,1 Decimal × or : 10 Decimal × or : 100 Decimal × or : 1.000
• European Format Mixed Multiplying/Dividing Decimal Numbers By Powers Of Ten (Exponent Form) Decimal × or : All Powers of Ten (Exponent Form) Decimal × or : All Positive Powers of Ten (Exponent Form) Decimal × or : All Negative Powers of Ten (Exponent Form) Decimal × or : 10 -3 Decimal × or : 10 -2 Decimal × or : 10 -1 Decimal × or : 10 1 Decimal × or : 10 2 Decimal × or : 10 3

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Powers of Ten Worksheet

Related Pages Math Worksheets Lessons for Fourth Grade Free Printable Worksheets

Powers of Ten Worksheets

In these free math worksheets, students practice how to calculate the powers of 10 (write the powers of 10 in standard form and exponential form).

How to calculate the powers of 10?

To calculate powers of 10, you can write 1 followed by the number of zeros corresponding to the power.

For example: 10 1 = 10 10 2 = 100 10 3 = 1,000 10 4 = 10,000 10 5 = 100,000 10 6 = 1,000,000

In general, for any positive integer n, 10 n can be calculated by writing a “1” followed by n zeros.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Powers of Ten Worksheet Worksheets .

More Powers of Ten Worksheets

Printable Powers of Ten Worksheet (Answers on the second page.)

Multiply by Powers of 10 (eg. 4 × 10 3 =) Multiply Decimals by Powers of 10 (eg. 3.2 × 10 3 =) Divide Decimals by Powers of 10 (eg. 74.2 ÷ 10 3 =)

Online Multiply by Powers of 10 Divide by Powers of 10

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Exponents and Powers of Ten Online practice for grades 5-8

This page provides online practice for exponents and evaluating powers. For example, you would find the value of $\big(\frac{1}{2}\big)^3$ or $10^6$.

(An exponent is the little elevated number in this expression: $2^4$. It indicates how many times the base number (in our case 2) is multiplied by itself. So, $2^4$ means $2\times2\times2\times2=16$.)

Options for the online practice include positive, zero, and negative exponents; whole-number, fractional, or decimal bases; and positive or negative bases.

You can evaluate powers (expressions with exponents), evaluate expressions where we multiply a power of ten by some factor, or do both.

You can choose timed or untimed practice, and the number of practice problems.

Give your answer as a fraction.

Generate quick link.

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Powers of ten

Exponent worksheets.

These grade 5 worksheets review reading and writing powers of ten , with varying formats and levels of difficulty.

5.31 x 10^3 =

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Understanding Powers of 10 in Fifth Grade Math

In fifth grade math, students encounter the concept of Powers of 10, which involves understanding the exponential notation where 10 is multiplied by itself a certain number of times. This concept plays a crucial role in understanding place value, scientific notation, and operations with very large or very small numbers. Powers of 10 provide a systematic way to represent numbers and help students comprehend the magnitude of quantities across various contexts. Mastery of Powers of 10 lays a strong foundation for more advanced mathematical concepts and real-world applications, making it an essential skill for 5th-grade students to develop.

Teaching Strategies for Powers of 10 in the Classroom

Educators utilize various strategies to teach Powers of 10 effectively in the 5th-grade classroom. Interactive lessons that incorporate visual aids, such as place value charts or manipulatives, help students visualize the concept of exponential notation. Engaging activities, such as Powers of 10 games or interactive worksheets, provide opportunities for hands-on practice and reinforce learning. Additionally, incorporating real-world examples and problem-solving tasks into lessons helps students understand the practical applications of Powers of 10. By providing a mix of interactive, hands-on, and real-world learning experiences, educators ensure that students develop a solid understanding of Powers of 10.

Practicing Powers of 10 with iKnowIt.com

iKnowIt.com offers an online platform for fifth-grade students to practice and reinforce their understanding of Powers of 10 in an engaging and interactive way. Through interactive games and exercises, students can explore the concept of Powers of 10 and strengthen their skills. The platform provides a variety of activities designed to cater to different learning styles and abilities, such as Powers of 10 quizzes and interactive lessons. With immediate feedback and progress tracking features, students can monitor their performance and track their improvement over time. iKnowIt.com's interactive approach to learning ensures that students develop a solid foundation in Powers of 10 while having fun.

This interactive math lesson is categorized as Level E. It may be best suited for fifth grade students.

Common Core Standard

5.NBT.2, MA.6.NSO.3.4, 5.4A Number And Operations In Base Ten Understand The Place Value System. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

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Equivalent Fractions (Level D) Learn how to determine if fractions are equal or not equal in this lesson.

Exponents (Level E) Learn about exponents and why they are useful in this math lesson.

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Powers of 10

The powers of 10 refer to the numbers in which the base is 10 and the exponent is an integer. For example, 10 2 , 10 3 , 10 6 show the different powers of 10. This can be understood with the concept that when 10 is multiplied a specific number of times, then it can be expressed in the form of exponents and those are called the powers of 10. Let us learn more about the powers of 10 in this page.

What does Powers of 10 mean?

The powers of 10 means when 10 is multiplied a certain number of times, the product can be expressed using exponents. These numbers which are written as exponents are the powers of 10. If we multiply 10 a couple of times it becomes difficult to write the number as in this case, 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000. Now, if we need to multiply 10 thirty times, it would be even more difficult to write the product with so many zeros. Therefore, exponents help to express this easily and this value (10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000) can be expressed as 10 9 . Here, 10 is the base and 9 is the power and this is read as 10 to the ninth power. Now, let us try to understand it the other way round. For example, 10 to the 7th power means 10 7 . This means that we need to multiply 10 seven times, that is, 10 7 = 10 × 10 × 10 × 10 × 10 × 10 × 10

This can be explained in another way.

The powers of 10 are of the form 10 x , where x is an integer. 10 x is read as '10 to the power of x'. If x is positive, we simplify 10 x by multiplying 10 by itself x times. For example, 10 3 = 10 × 10 ×10 (3 times) = 1000. If x is negative, then we apply the property of exponents, a -m = 1/a m and then we apply the same logic as explained earlier. For example 10 -3 = 1/10 3 = (1/10) 3 = 1/10 × 1/10 × 1/10 = 1/1000 = 0.001. By using these two examples, we can conclude two things that are very useful to calculate the powers of 10.

• When the power is positive, 10 x = '1 followed by x number of zeros'. For example, 10 6 = 1,000,000. Here, there are 6 zeros placed after 1 because the power of 10 is 6.
• When the power is negative, 10 -x = '0 point followed by (x -1) number of zeros followed by 1". For example, 10 -6 = 0.000001. Here, we placed 5 zeros after the decimal point (followed by 1) as the power was a negative 6 and 6 - 1 = 5.

10 to the Power of 2

10 to the power of 2 is also called the second power of ten. This is written as 10 2 and this means that 10 is multiplied two times. In other words, 10 × 10 = 10 2 . Here 10 is the base and 2 is the exponent. This can be further evaluated as 10 2 = 100.

10 to the Power of 3

10 to the power of 3 is called the third power of ten and is written as 10 3 . This means, 10 × 10 × 10 = 10 3 . In this expression, 10 to the third power, 10 is the base and 3 is its power or exponent. This can also be evaluated as 10 3 = 1000.

10 to the Power of 1

10 to the power of 1 means the first power of ten which is 10 1 . We know that any number to the power of 1 means it is the number itself. So here, 10 1 = 10.

Powers of 10 Chart

The powers of 10 chart shows that the different powers of 10 have different values. For example, if we write 10 5 in the expanded form, it will be 10 5 = 10 × 10 × 10 × 10 × 10. Now, the value of 10 5 in the decimal form will be 100000. And if we write it in the form of a fraction it will be 100000/1. Similarly, if we write 10 -5 in the expanded form, it will be 10 -5 = 1/(10 × 10 × 10 × 10 × 10). Now, the value of 10 -5 in the decimal form will be 0.00001. And if we write it in the form of a fraction it will be 1/100000. The following table shows the powers of 10 chart which includes positive powers and negative powers.

Positive Powers of 10

The powers of 10 have some specific names (though not all powers) for some specific powers. For example, 10 6 (10 to the power of 6) is known as a 'million' and the SI prefix of 10 power 6 is 'giga' which is represented by the SI symbol G. Similarly, we have some specific names for some positive powers of 10 which are given in the following table.

Negative Powers of 10

The negative powers of 10 are expressed in a different way. We know that a negative power ( negative exponent ) is defined as the multiplicative inverse of the base. This means that we write the reciprocal of the number and then solve it like positive exponents. For example, (4/5) -2 can be written as (5/4) 2 . Similarly, a negative power of 10, like 10 -3 , can be written as 1/10 3 , or, 1/(10 × 10 × 10) = 1/1000 = 0.001

Just like how we have some peculiar names for positive powers of 10, we have some names for some negative powers of 10 as well. A few of them are given in the following table.

2 to the Power of 10

It should be noted that 2 to the power of 10 is not the same as 10 to the power of 2. 2 to the power of 10 means a number in which 2 is the base and 10 is the exponent. This is written as 2 10 and this means 2 is multiplied ten times, that is, 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024.

Calculating Powers of 10

In order to calculate the sum, difference, product, and quotient of powers of 10, we can first find the values of powers of 10 and then do the respective operation. For example, 10 3 /10 2 = 1000/100 = 10. But sometimes, this procedure is difficult if the exponent is very large. In such cases, the following procedures would help.

Adding and Subtracting Powers of 10

To add and subtract powers of 10, we take the minimum power of 10 as the common factor and then simplify the rest. For example,

• 10 5 + 10 8 = 10 5 (1 + 10 3 ) = 10 5 (1 + 1000) = 10 5 (1001) = 100,100,000

Multiplying Powers of 10

To multiply the powers of 10, we apply an exponent rule that says a m × a n = a m + n . This rule says that we need to add the exponents when the bases are the same. Hence, this rule can be applied to multiply two or more powers of 10. Here are some examples.

• 10 5 × 10 8 = 10 5 + 8 = 10 13
• 10 -3 × 10 6 = 10 -3 + 6 = 10 3

Dividing Powers of 10

There is a rule of exponents, a m / a n = a m - n . We use this rule to divide the powers of 10. This rule says that we need to subtract the powers when the bases are the same. Here are a few examples.

• 10 17 / 10 15 = 10 17 - 15 = 10 2 = 100
• 10 -6 / 10 -12 = 10 -6 + 12 = 10 6

Important Tips on Powers of 10

• Powers of 10 refer to numbers like 10 5 , or 10 6 , where 10 is the base and 5 and 6 are its powers.
• 2 to the power of 10 means a number in which 2 is the base and 10 is the exponent, that is, 2 10 .
• Just like 2 to the power of 10 means 2 10 , other phrases like 3 to the power of 10 means 3 10 , 4 to the power of 10 means 4 10 . These should not be confused with the powers of 10 that we have studied on this page.

☛ Related Topics

• Exponent Rules
• Multiplying Exponents
• How to Express 10 to the Power of 10?

Powers of 10 Examples

Example 1: Which of the following is equivalent to 100000?

Solution: In 100000, there are 5 zeros. This gives us a clue that we can express it as the 5th power of 10. This means 10 5 . Therefore, the correct option is (a.) 10 5

Example 2: Select the exponent which will make this equation true. 10 ? = 1

a.) Any number to the power of 1 is always equal to the number itself. This means 10 1 = 10. Therefore, this is not the correct option.

b.) 10 4 is equal to 10000. Therefore, this is not the correct option.

c.) We know that any number to the power of zero is always equal to 1. Therefore, 10 0 = 1. It means this option is the correct answer and the missing exponent is 0.

Example 3: State true or false.

a.) 3 to the power of 10 means 3 10

b.) The second power of 10 means 10 2

a.) True, 3 to the power of 10 means 3 10

b.) True, the second power of 10 means 10 2

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Practice Questions on Power of 10

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FAQs on Power of 10

What are the powers of 10 in math.

Powers of 10 refer to the numbers in which 10 is the base and any integer is the exponent. For example, 10 3 , 10 6 , 10 -7 are a few examples of the powers of 10.

How much is 10 to the Power of 10?

10 to the power of 10 means an expression in which 10 is the base and 10 is the exponent. This can be expressed as 10 10 and this means 10 is multiplied 10 times, that is, 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 which is equal to 10000000000.

How to Convert 0.00001 to the power of 10?

In order to convert 0.00001 to the power of 10, first, we need to convert this decimal into its fraction form. This will make it 1/100000. Now, this fraction can be written in an exponential form which will be 1/10 5 . This can be further expressed as a negative exponent,10 -5

How to Convert a Number to the Power of 10?

In order to convert a number to the power of 10, we write it in the scientific notation. For example, the number 5040000000000000 is a little difficult to write and it would be easier if we write it in the standard form where we use the powers of 10. So this is expressed as 5.04 × 10 15 . Let us see how to write this number in the standard exponential form , using the following steps:

• Step 1: Count the number of trailing zeros in the given number. In the given number, 5040000000000000, the number of trailing zeros are 13.
• Step 2: Use the beginning part of the given number and write the digits from the left till the last non-zero digit, followed by a 10 raised to a power that is equal to the number of trailing zeros. This means 504 and 10 13
• Step 3: Place a decimal point after the first digit from the left side and add the number of decimal places that are created, to the power of 10 which is written. Here, we will place a decimal point after 5, and it will become 5.04. Since there are 2 decimal places created in 5.04, we will add 2 to the existing power of 10. The existing power of 10 was 13 because there were 13 trailing zeros, but now it will become 15. This will make it 5.04 × 10 15 . Therefore, 5040000000000000 can be written as 5.04 × 10 15

How to write 100 as a Power of 10?

In order to write 100 as a power of 10, we will first count the number of zeros in 100, which is two. This means 100 = 10 × 10. Therefore, 100 as a power of 10 can be written as 10 2

What is the Second Power of 10?

The second power of 10 can be written as 10 2 . This is also known as 10 to the power of 2 and is equal to 100 because 10 2 = 10 × 10 = 100.

What is the First Power of 10?

The first power of 10 is written as 10 1 . This is also read as 10 to the power of 1 and we know that any number to the power of 1 is the number itself, so 10 1 = 10.

How to Multiply Decimals by Powers of 10?

In order to multiply decimals by powers of 10, we need to remember a simple rule. We express the product in such a way that we write the given decimal number and move the decimal point to the right according to the number given as the exponent of 10. If the exponent of 10 is 3, we will write the given number and move the decimal 3 places to the right to get the answer easily. For example, if we need to multiply 46.3 × 10 4 , we can see that the exponent of 10 is 4, so we will move the decimal point 4 places to the right. This means, 46.3 × 10 4 = 463000.

How much is 2 to the Power of 10?

2 to the power of 10 means an expression where 2 is the base and 10 is the exponent. This can be expressed as 2 10 and this means that 2 is multiplied ten times, that is, 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024.

How to Write a Given Number as a Power of 10?

• To express a given number (>1) as a power of 10, just write it as 10 n (n being positive) where 'n' is the number of zeros after 1 in the given number. For example, 10000 = 10 4 .
• To express a given number (<1) as a power of 10, just count the number of zeros after '0 point' and before '1', add 1 to the result, and then put that number along with the negative sign as the exponent of 10. For example, 0.001 = 10 -3 (as there are 2 zeros after 0 point and before 1 in 0.001).

What is the Difference Between 2 to the Power of 10 and 10 to the Power of 2?

2 to the power of 10 = 2 10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024 whereas 10 to the power of 2 is 10 2 = 10 × 10 = 100. Thus,

• 2 to the power of 10 = 1,024
• 10 to the power of 2 = 100

How to Find the Powers of 10?

To find the powers of 10 , we use the following shortcuts depending upon whether the exponent is positive or negative.

• If the exponent is positive, then 10 n = '1 followed by 'n' zeros'. For example, 10 4 = 10000.
• If the exponent is negative, then 10 n = '0 point followed by (n - 1) zeros followed by 1'. For example, 10 -4 = 0.0001.

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Power of 10

Introduction to Power of 10

The power of ten, in math, any of the integer (whole-valued) exponents of the number 10. A power of 10 is as many number 10s as designated by the exponent multiplied together. Therefore, shown in long-form, a power of ten is the number 1 subsequent to n zeros, in which ‘n’ is the exponent and is greater than 0; for example, 10 6 is mathematically written as 1,000,000. When n is less than 0, the power of 10 is the number 1 n placed followed by the decimal point; for example, 10 −3 is written 0.001.

Power of 10 to Zero

When n equals to 0, the power of 10 will be 1; i.e., 10 0 = 1. Refer to the below table for expressions in positives and negative powers of 10.

Powers of 10

Multiplying and Dividing Powers of 10

Maybe you're not sure that it's useful to be able to write numbers in powers of ten math or mega 10 powers. Well, powers of ten math are quite helpful when performing math calculations, as well. Let's say if we ask you ''what are 10 times 1,000?'' Hardly anything- it's just 10,000. But what if we ask ''what will be one trillion times one quadrillion?''

It concludes that the multiplication of really large numbers is easy with powers of ten. All you need to do is to add up the exponents, and you're sorted. Let's consider the example we just quoted above. What is one trillion times one quadrillion? First, one trillion is 10 12 , and one quadrillion is 10 15 . So the correct answer is 10 27 , which is a huge number. Now, you can see that almost immediately, without requiring a calculator, we did it shorthand.

Power of Ten Prefixes

When a numerical digit represents a quantity instead of a count, SI prefixes can be used - therefore "femtosecond", not "one quadrillionth of a second'' - although most frequently powers of 10 are used rather than some of the very low and very high prefixes. In certain cases, specialized units are taken help of, such as the light-year particle physicists barn or the astronomer's parsec.

Nonetheless, large numbers carry an intellectual intrigue and are of mathematical interest, and assigning them names is one of the ways in which most of us try to conceptualize and understand them.

Solved Examples

Solve the following expressions:

Log (10 6 ) = 6

Log (10 27 ) = 27

Log (10 365.2748 ) = 365.2748

Log (10 -5 ) = -5

Log (x) -5 → x = 10 5

Log (x) = 6.789 → x = 10 6.789

Log (x) = -2.23 → x = 10 -2.23

The power of 10 is easy to remember since we use base 10 of a number system.

For 10 n having ‘n’ a positive integer, just write "1" with n zeros after it. For negative powers 10 −n , write “0" followed by n−1 zeros, and then a 1. The powers of 10 are extensively used in scientific notation.

Let's take a number 10. We could take two 10s and multiply them together, which means 10 times 10, which you know is equal to 100. We could also take three 10s and multiply them together, 10 times 10 times 10 which is equal to one thousand. And we could do this with any number of 10s. But at some point, if we do this with enough 10s, it will get pretty hard for us to write. So let's give an example. Let's say I were to do this with ten 10s, so if I were to go 10 times 10 just like this :  10×10×10×10×10×10×10×10×10. This is going to be equal to even the number that is equal to, is going to be quite hard to write. It is  going to be one that is followed by ten zeros. This will be 10 billion. And it's already getting hard to write. And imagine if you have thirty 10s that we were multiplying together, it will be very much difficult to calculate or write down like this.

The mathematicians have come up with some notations and some ideas to be able to write things like this, a little bit more elegantly. So the way they do this is through something which is  known as exponents. And so 10 times 10, we can rewrite as being equal to, if I have two 10s and I'm multiplying them together, I could write this as 10 to the second power. That's how we can pronounce it as 10 to the power 2. It looks quite fancy but all that means is let's take two 10s and multiply them together and we are going to get one hundred. In this, the two would be called as exponents and the 10 would be the base. So eventually, 10 to the second power of 10 times 10 is equal to hundred. 

So how would you write 10 times 10 times 10 or 10000 ? How are you going to write that by using exponents ? We are taking three numbers of 10s and multiplying them together, this would be 10 to the third power. Here, ten is the base and three is the exponent. We would read this as 10 to the third power. If you will ever see 10 to the third power, that means we can multiply 10 times 10 times 10 which is the same thing as one thousand. So this is another way of writing 1000. 

FAQs on Power of 10

1. What is Meant by Logarithm?

Logarithm, the power or exponent to which a base should be raised to produce a given number. Written mathematically, x is the logarithm of n to the base b if b x = n, where case one writes x = log b n. For example, 2 4 = 16; thus, 4 is the logarithm of 16 to base 2, or 4 = log 2 16. Similarly, since 10 3 = 1000, then 3 = log 10 1000. Logarithms of the second-mentioned sort (that is, logarithms with base 10) are known as common, or Briggsian, logarithms and are simply written log n.

2. What is the importance of ‘logs’ in powers?

Are you assuming if there's an opposite to powers of 10? Something like how multiplication is the opposite of division or addition is the opposite of subtraction. It appears that there is such a thing called: ``logs'' or “logarithms”. Logs initially emerged to be important for multiplying and dividing and were used all the time in performing arithmetic operations with the help of slide rules. Now that calculators are commonplace, the use of logarithms for fundamental calculations is steadily disappearing, but it can still be worthwhile. And while employing logarithms for simple arithmetic calculations is not so common, there are other uses for logarithms in many areas of science.

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Powers of Ten Problem Solving worksheet

Total reviews: (0), powers of ten problem solving worksheet description.

Perfect to use after a series of lessons on powers of ten and standard form, this worksheet provides some problem-solving activities for learners to apply their skills.

Section A features a completion table involving decimal numbers and numbers in standard form.

Section B then provides a worded problem involving ratios of scale and volume.

Section C then has another worded problem again involving a ratio.

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Powers of Ten – Definition with Examples

Power of 10 – introduction, what is the power of ten, positive and negative exponents, solved examples, practice problem , frequently asked questions.

Ms. Kelly wrote a few equations on the board and asked her students to look for a pattern in them. 

$10 × 1 = 10$

$10 × 10 = 100$

$10 × 10 × 10 = 1,000$

$10 × 10 × 10 × 10 = 10,000$

$10 × 10 × 10 × 10 × 10 × 10 = 100,000$

Let’s observe the equations together. Each equation is ten times more than the previous one. Also, the number of zeros in the product of each equation is the same as in the number of tens multiplied together. 

When we multiply 10 by itself a certain number of times, we call it the power of ten . Let’s explore more about them right away!

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An exponent of a number indicates how many times we multiply a number by itself. When we multiply 10 by itself a certain number of times, we can express that in an exponent form, also called the power of 10. Like any other exponential form, a power of 10 consists of a base and an exponent, as shown below.

• The base of power tells us what number is being multiplied. In this case, the base is always 10.
• The exponent tells us how many times the base is multiplied by itself. The exponent can be any integer (positive, negative, or zero). 

For example, 10 n has base 10 and exponent n, where n is an integer. 10 n is read as “10 to the power of n.”

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Expanded Form

Power of any number is an expression that represents repeated multiplication of the number. It is represented as x n . The exponent of the power tells us how many times the number is multiplied to itself. 

For example, when the exponent is 3 , we multiply 10 by itself 3 times. 

10 3 = 10 × 10 × 10, this is also called the expanded form of the power.

The exponent of a power of ten can be a positive or negative integer. When the exponent is positive, we can write the power in the expanded form and find the product. 

For example, 10 4 = 10 × 10 × 10 × 10 = 10,000. The number of zeros in the product is equal to the exponent.

When the exponent is negative, we can apply the rules of exponent, x -a  = 1/x a , and find the value. 

For example, 10 -4 = 1/10 4  = 1/10000 = 0.0001

In general, we can write the value in decimals by observing the exponent. The value is a decimal point followed by as many zeros as one less than the exponent and a 1. When the exponent is negative, the value is always less than 1.

Any number raised to the power 0 is one, and ten is no exception. When the exponent is 0, the value is 1. 

What Is the Use of Powers of Ten?

Scientists and engineers often encounter very big or small numbers. For example, if scientists have to send a spacecraft to the moon, it should travel at least 240,000 miles, which is the distance between Earth and the Moon. Such numbers can be troublesome to use in their original form. So, scientists use a notation where they write the number in terms of the power of 10. For example, a large number like 50,000,000 can be represented as 5 × 10 7 . 

A complicated number like 456,000 can be written as 456 × 10 3 or 4.56 × 10 5 , which is a scientific notation. 

A scientific notation of a positive number is to express the number as the product of a number less than 10 and a power of 10. In case the number is greater than 1, then the exponent (in the scientific notation) is a positive number. If the number is less than 1, then the exponent will be a negative number. For example, a small number like 0.00005 can be written as 5 × 10 -5 .

Example 1: Write 10,000,000 as a power of 10.

Solution: There are 7 zeros in 10,000,000. So, we can write the given number as 7th power of ten or 10 7 .

Example 2: Find the product of 5.65 × 10⁴.  

Solution: When multiplying the number by the power of 10, we move the decimal points to the right side.

So, 5.65 × 10000 = 56,500

Example 3: George and Melissa are contending for the position of mayor. The total number of votes cast for each candidate is:

George:  7 × 10⁴

Melissa: 10 5

Who won the election? 

Solution: George received  7 × 10⁴ or 70,000 votes

Melissa got 10 5  or 100,000 votes.

Clearly, Melissa won the election.

Power of 10 - Definition with Example

Attend this quiz & Test your knowledge.

Find the value of n that would make the equation true. $10^{n} = 100,000$

Which of the following numbers is equivalent to $10^{4}$, which of the following is greater than 10.

What is the difference between 10 2  and 2 10 ?

In 10 2 , the base is 10, and the exponent is 2. That is, ten is being multiplied to itself twice. 10 2 = 10 × 10 = 100. In 2 10 , the base is 2, and the exponent is 10. That is, 2 is being multiplied to itself ten times. 2 10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

Is 10 4 equal to 10 -4 ?

No, different powers of 10 have different values.  10 4 = 10000 and 10 -4 = 1/10000 So, they both are different, and 10 4 > 10 -4 Also, since the exponent of 10 4 is 4 > 1, the value of the power is greater than 10.Since the exponent of 10 -4 is negative, the value of the power is less than 1.

How can we write the expanded form 18964 as the power of ten?

The expanded form of 18964 = 10000 + 8000 + 900 + 60 + 4 = 10 4 + 8 × 10 3 + 9 × 10 3 + 6 × 10 + 4

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Exponents And Powers

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 3 4 , where 4 is the exponent and 3 is the base. The whole expression 3 4 is said to be power. Also learn  the  laws of exponents here.

Basically, power is an expression that shows repeated multiplication of the same number or factor. The value of the exponent is based on the number of times the base is multiplied to itself. See of the examples here:

What is Exponent?

An exponent of a number, represents the number of times the number is multiplied to itself. If 8 is multiplied by itself for n times, then, it is represented as:

8 x 8 x 8 x 8 x …..n times = 8 n

The above expression, 8 n , is said as 8 raised to the power n. Therefore, exponents are also called power or sometimes indices.

• 2 x 2 x 2 x 2 = 2 4
• 5 x 5 x 5 = 5 3
• 10 x 10 x 10 x 10 x 10 x 10 = 10 6

General Form of Exponents

The exponent is a simple but powerful tool. It tells us how many times a number should be multiplied by itself to get the desired result. Thus any number ‘a’ raised to power ‘n’ can be expressed as:

Here a is any number and n is a natural number.

a n  is also called the nth power of a .

‘a’ is the base and ‘n’ is the exponent or index or power.

 ‘a’ is multiplied ‘n’ times, and thereby exponentiation is the shorthand method of repeated multiplication.

Also, read:

• Exponents and Powers for Class 7
• Exponents And Powers for Class 8

Laws of Exponents

The laws of exponents are demonstrated based on the powers they carry.

• Bases – multiplying the like ones – add the exponents and keep the base same. (Multiplication Law)
• Bases – raise it with power to another – multiply the exponents and keep the base same.
• Bases – dividing the like ones – ‘Numerator Exponent – Denominator Exponent’ and keep the base same. (Division Law)

Let ‘a’ is any number or integer (positive or negative) and ‘m’,  ‘n’ are positive integers, denoting the power to the bases, then;

Multiplication Law

As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers.

           a m  × a n   = a m+n

Division Law

When two exponents having same bases and different powers are divided, then it results in base raised to the difference between the two powers.

          a m ÷ a n   = a m  / a n   = a m-n

Negative Exponent Law

Any base if has a negative power, then it results in reciprocal but with positive power or integer to the base.

            a -m    = 1/a m  

Rules of Exponents

The rules of exponents are followed by the laws. Let us have a look at them with a brief explanation.

Suppose ‘a’ & ‘b’ are the integers and ‘m’ & ‘n’ are the values for powers, then the rules for exponents and powers are given by:

i) a 0  = 1

As per this rule, if the power of any integer is zero, then the resulted output will be unity or one.

Example: 5 0 = 1

ii) (a m ) n  = a( mn )

‘a’ raised to the power ‘m’ raised to the power ‘n’ is equal to ‘a’ raised to the power product of ‘m’ and ‘n’.

Example: (5 2 ) 3  = 5 2 x 3

iii) a m  × b m  =(ab) m

The product of ‘a’ raised to the power of ‘m’ and ‘b’ raised to the power ‘m’ is equal to the product of ‘a’ and ‘b’ whole raised to the power ‘m’.

Example:  5 2  × 6 2  =(5 x 6) 2

iv) a m /b m  = (a/b) m

The division of ‘a’ raised to the power ‘m’ and ‘b’ raised to the power ‘m’ is equal to the division of ‘a’ by ‘b’ whole raised to the power ‘m’.

Example:  5 2 /6 2  = (5/6) 2

Solved Questions

Example 1: Write 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 in exponent form.

In this problem 7s are written 8 times, so the problem can be rewritten as an exponent of 8.

7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 7 8 .

Example 2 : Write below problems like exponents:

• 3 x 3 x 3 x 3 x 3 x 3
• 7 x 7 x 7 x 7 x 7
• 10 x 10 x 10 x 10 x 10 x 10 x 10
• 3 x 3 x 3 x 3 x 3 x 3 = 3 6
• 7 x 7 x 7 x 7 x 7 = 7 5
• 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 7  

Example 3: Simplify 25 3 /5 3  

 Using Law: a m /b m  = (a/b) m

25 3 /5 3   can be written as (25/5) 3   = 5 3  = 125.

Exponents and Powers Applications

Scientific notation uses the power of ten expressed as exponents, so we need a little background before we can jump in. In this concept, we round out your knowledge of exponents, which we studied in previous classes.

The distance between the Sun and the Earth is 149,600,000 kilometres. The mass of the Sun is 1,989,000,000,000,000,000,000,000,000,000 kilograms. The age of the Earth is 4,550,000,000 years. These numbers are way too large or small to memorize in this way.  With the help of exponents and powers, these huge numbers can be reduced to a very compact form and can be easily expressed in powers of 10.

Now, coming back to the examples we mentioned above, we can express the distance between the Sun and the Earth with the help of exponents and powers as following:

Distance between the Sun and the Earth 149,600,000 = 1.496× 10 × 10 × 10 × 10 × 10× 10 × 10 = 1.496× 10 8 kilometers.

Mass of the Sun: 1,989,000,000,000,000,000,000,000,000,000 kilograms = 1.989 × 10 30  kilograms.

Age of the Earth:  4,550,000,000 years = 4. 55× 10 9  years

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What is the Power of 10?

"The powers of 10 refer to a number where 10 is a base and the exponent is an integer." The power of 10 means when 10 is multiplied by a certain number of times, you can express the number as a product of 10.

For example, if you multiply the 10 to 9 times 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000.

Then the number is difficult to read, but 10^9 makes it easy to read and write. Here 10 is the base and 9 is the exponent of the number to write the number 1000000000. You can express the 10^9 as a billion with the 10 to the power 9 with the power of 10 calculator .

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Let’s convert 10 to the power of 7 and 10 to the power of 3!

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The Power of 10 Prefixes:

The power of ten is commonly used in business and calculation. For example, the power 10 exponent 3 is Thousand, the 10 to the power 6 is million, and so on. The various prefixes used for the power of 10 and their names are given below in the table.

What is 10 to the Power of 3?

The power of the 10 to the exponent value 3 is 1000.

How can you Find 10 to the Power of 10?

You can find the 10 to the power of 10 by multiplying the 10 ten times.

What is 10 to the Power of 2?

The 10 to the power of 2 means 100 by multiplying 10 two times.

What is Meant by 2 to the Power of 10?

2 to the power of 10 means that 2 is the base and 10 is the exponent. This is written as 2^10, and multiply the 2 ten times with each other.

Like that: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

References:

From the source of Wikipedia: Power of 10 , How to find power of 10?  From the source of Hellothinkster: 2 power of 10 , What is the power of 10?

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The Power of Teamwork in Entrepreneurship

The power of teamwork in entrepreneurship is a subject of increasing interest and importance. Contrary to the conventional notion of entrepreneurship as an individual pursuit, contemporary understanding emphasizes the role of collective effort. Successful entrepreneurs recognize the merits of assembling a robust and diverse team, as collaboration within a team fosters innovative ideas and effective problem-solving. Team dynamics significantly influence entrepreneurial endeavors, with effective communication, trust, and mutual respect being vital for cohesive teams. Nonetheless, teamwork in entrepreneurship presents challenges, including conflicts and disagreements that must be resolved for sustained productivity. Despite these challenges, the benefits of teamwork in entrepreneurship are manifold, including enhanced creativity, problem-solving abilities, and motivation in the face of adversity. Building and managing a successful entrepreneurial team necessitates careful selection, diversity in skills and perspectives, effective leadership, regular evaluation and feedback, and continuous learning and development opportunities. This article explores the power of teamwork in entrepreneurship, its role in entrepreneurial success, and the strategies to foster and maintain effective teamwork.

Table of Contents

Key Takeaways

• Entrepreneurship is not just about individual achievement, but also about the collective effort of a team.
• Collaboration within a team can lead to innovative ideas and problem-solving.
• Effective communication and trust among team members foster a positive working environment.
• Diversity in skills, backgrounds, and perspectives can contribute to a well-rounded and successful entrepreneurial team.

The Role of Teamwork in Entrepreneurial Success

The role of teamwork in entrepreneurial success is crucial as it allows for the integration of diverse skills, perspectives, and experiences within a well-functioning team, fostering collaboration, innovative ideas, and problem-solving abilities. Leveraging team dynamics for entrepreneurial innovation is a key aspect of this process. Effective communication plays a vital role in entrepreneurial teams, as it enables the exchange of ideas, information, and feedback among team members. Clear and open communication channels facilitate the sharing of knowledge and expertise, leading to improved decision-making and problem-solving. Moreover, effective communication helps in building trust and mutual understanding among team members, creating a supportive and cohesive work environment. By leveraging team dynamics and promoting effective communication, entrepreneurial teams can enhance their performance, adaptability, and overall success in achieving their goals.

Leveraging Team Dynamics for Entrepreneurial Growth

Leveraging team dynamics can significantly contribute to the growth and success of entrepreneurial ventures. Maximizing collaboration and harnessing diversity within a team can lead to innovative ideas and problem-solving. Effective communication and collaboration are essential for a cohesive team that can bring together different skills, perspectives, and experiences. By establishing clearly defined roles and responsibilities, team members can work together towards common goals. Trust and mutual respect among team members foster a positive working environment, enabling the team to overcome challenges and conflicts. A well-balanced team, with a diverse range of skills and expertise, enhances its overall performance. The benefits of teamwork in entrepreneurship include increased creativity and problem-solving abilities. A supportive team can provide motivation and encouragement during challenging times, contributing to the long-term success of the entrepreneurial venture.

The Importance of Clear Roles and Responsibilities in Entrepreneurial Teams

Establishing clear roles and responsibilities within entrepreneurial teams is crucial for effective collaboration and goal achievement. Clear roles enable team members to understand their individual responsibilities and contribute to the team’s overall objectives. Effective communication is essential in ensuring that everyone is on the same page and understands their role in the team’s success. By clearly defining roles, team members can avoid confusion, duplication of efforts, and conflicts that may arise due to overlapping responsibilities. Furthermore, clear roles facilitate effective decision-making processes, as team members know who is responsible for what aspects of the venture. Effective communication within the team ensures that information flows smoothly, enabling timely decision-making and problem-solving. Overall, establishing clear roles and promoting effective communication are vital for successful collaboration and the achievement of entrepreneurial goals.

Communication and Collaboration: Key Pillars of Entrepreneurial Teamwork

Effective communication and collaboration are essential components of successful entrepreneurial teamwork. In order for a team to work cohesively and efficiently, members must employ effective communication strategies and collaboration techniques. Communication strategies involve clear and concise information sharing, active listening, and mutual understanding. This can be achieved through regular team meetings, open and honest communication channels, and the use of appropriate communication tools. Collaboration techniques involve working together towards a common goal, leveraging each member’s strengths, and fostering a sense of shared responsibility. This can be achieved through effective delegation, regular feedback and brainstorming sessions, and encouraging a culture of collaboration and trust. By implementing these communication strategies and collaboration techniques, entrepreneurial teams can enhance their overall performance and achieve successful outcomes.

Fostering Trust and Mutual Respect in Entrepreneurship Teams

Fostering a culture of trust and mutual respect is crucial for creating a harmonious and productive work environment within entrepreneurship teams. Effective communication, building trust, and collaboration are key elements in achieving this culture.

• Open and transparent communication allows team members to express their ideas, concerns, and suggestions freely.
• Building trust involves creating an environment where individuals feel safe to take risks and share their opinions.
• Collaboration encourages teamwork and the pooling of diverse skills and perspectives to solve problems and innovate.
• By fostering effective communication, team members can better understand each other’s strengths and weaknesses, leading to better task allocation and performance.
• Building trust and collaboration within entrepreneurship teams promotes a sense of unity, motivation, and shared responsibility towards achieving common goals.

Overall, creating a culture of trust and mutual respect is essential for enhancing team dynamics and driving the success of entrepreneurial ventures.

Enhancing Performance Through Skillful Team Composition

Team composition plays a crucial role in maximizing productivity and optimizing collaboration in entrepreneurship. The selection of team members should be based on their skills, expertise, and diverse backgrounds. A well-rounded team with a balance of complementary skills can enhance the overall performance of the team. Effective leadership is essential in guiding and managing the team towards its goals. Regular evaluation and feedback help identify areas for improvement within the team and contribute to its long-term success. By carefully selecting team members and promoting diversity, entrepreneurship teams can tap into the collective knowledge and expertise of its members, leading to increased creativity, problem-solving abilities, and innovation. The skillful composition of teams in entrepreneurship is vital for achieving success and realizing the full potential of collaborative efforts.

Overcoming Challenges: Resolving Conflicts in Entrepreneurial Teams

Resolving conflicts within entrepreneurial teams requires open communication and a willingness to address divergent viewpoints. Conflict resolution strategies play a crucial role in promoting a positive work environment. Here are some effective strategies for resolving conflicts in entrepreneurial teams:

• Active listening: Team members should actively listen to each other’s perspectives without interrupting or judging.
• Collaboration: Encouraging team members to work together and find mutually agreeable solutions.
• Mediation : Involving a neutral third party to facilitate discussions and help find common ground.
• Constructive feedback: Providing feedback in a constructive manner to address issues and promote growth.
• Conflict resolution training: Offering training sessions to team members to enhance their conflict resolution skills.

Adaptability and Feedback: Essential Traits for Entrepreneurial Team Members

In the context of entrepreneurial teams, adaptability and feedback are essential traits for team members. Adaptability refers to the ability to adjust to new situations, challenges, and ideas. It enables team members to respond effectively to changing market conditions and evolving business environments. In the entrepreneurial context, adaptability plays a crucial role in the success of ventures as it allows teams to be flexible and responsive to emerging opportunities. Feedback, on the other hand, provides valuable insights and information that can help team members refine their strategies and improve their performance. It facilitates learning and growth within the team, allowing members to identify areas for improvement and make necessary adjustments. Ultimately, both adaptability and feedback contribute to the overall success of entrepreneurial teams by fostering continuous improvement and innovation.

Unleashing Creativity and Problem-Solving Through Teamwork

Collaboration among individuals with diverse skills and perspectives can lead to the generation of innovative ideas and effective problem-solving. In the context of entrepreneurship, teamwork plays a crucial role in unleashing creativity and enhancing problem-solving abilities. To maximize team synergy and foster a culture of collaboration, the following strategies can be implemented:

• Encourage open and inclusive communication within the team.
• Create a supportive and trusting environment where team members feel comfortable sharing their ideas.
• Emphasize the value of brainstorming and encouraging different perspectives.
• Implement collaborative problem-solving techniques, such as design thinking or agile methodologies.
• Provide opportunities for cross-training and skill development to enhance the team’s overall capabilities.

The Power of Support: Motivation and Encouragement in Entrepreneurship

Motivation and encouragement are essential factors that contribute to the success of individuals in entrepreneurial endeavors. In the context of entrepreneurship, individuals often face numerous obstacles and challenges. A supportive environment that fosters motivation and encouragement can greatly assist individuals in overcoming these obstacles. Such an environment provides emotional support, guidance, and resources necessary for entrepreneurs to persevere and achieve their goals. Motivation is crucial in helping individuals maintain focus and drive, while encouragement instills confidence and a positive mindset. It creates a sense of belief in one’s abilities, leading to increased resilience and determination in the face of adversity. Moreover, a supportive environment can provide valuable feedback and mentorship, helping entrepreneurs navigate through challenges and learn from their experiences. Overall, motivation and encouragement within a supportive environment play a pivotal role in empowering individuals to overcome obstacles and succeed in their entrepreneurial endeavors.

Building Successful Entrepreneurial Teams: The Art of Selection

The previous subtopic emphasized the significance of support, motivation, and encouragement in entrepreneurship. In line with this, the current subtopic focuses on the critical aspect of building successful entrepreneurial teams through a careful selection process and team composition. This process involves several key factors that contribute to the overall effectiveness and performance of the team.

The selection process entails evaluating potential team members based on their skills, expertise, and compatibility with the team’s goals and values. It is essential to consider diversity in terms of skills, backgrounds, and perspectives to create a well-rounded team. Effective leadership plays a vital role in managing and guiding the team towards its objectives. Regular evaluation and feedback provide insights into areas that require improvement within the team. Additionally, continuous learning and development opportunities contribute to the long-term success of the team.

Embracing Diversity: Fueling Innovation in Entrepreneurial Teams

Diversity within entrepreneurial teams contributes to increased innovation and creativity. Fostering inclusion and harnessing diversity are essential for fueling innovation in entrepreneurial teams. Research has shown that diverse teams bring together a variety of perspectives, experiences, and skills, which can lead to the generation of novel ideas and approaches to problem-solving. By embracing diversity, entrepreneurial teams can tap into a broader range of knowledge and expertise, enabling them to adapt to changing market dynamics and develop innovative solutions. Moreover, diverse teams are more likely to challenge conventional thinking and avoid groupthink, leading to better decision-making processes. To fully harness the benefits of diversity, it is important for team leaders to create a supportive and inclusive environment where all team members feel valued and empowered to contribute their unique perspectives and insights.

Effective Leadership: Guiding Entrepreneurial Teams Towards Success

Effective leadership plays a crucial role in guiding and facilitating the success of entrepreneurial teams. Developing effective leadership skills is essential for entrepreneurs who aim to lead their teams effectively towards success. Here are five key aspects of effective leadership in guiding entrepreneurial teams:

Clear vision and direction: Effective leaders provide a clear vision and direction for the team, ensuring that everyone understands the goals and objectives.

Effective communication: Leaders should possess strong communication skills to effectively convey information, expectations, and feedback to team members.

Empowering and motivating: Leaders should empower team members by delegating responsibilities and providing autonomy while also motivating them to perform at their best.

Conflict resolution: Effective leaders are skilled in resolving conflicts within the team, addressing disagreements, and fostering a positive and collaborative work environment.

Continuous development: Leaders should continuously develop their own leadership skills and encourage the growth and development of their team members through training and mentorship opportunities.

Evaluating and Improving: Continuous Growth in Entrepreneurial Teams

Continuous growth in entrepreneurial teams involves evaluating and improving various aspects of team performance to enhance overall success. Evaluating the effectiveness of a team is essential to identify strengths, weaknesses, and areas for improvement. This evaluation process typically involves analyzing team dynamics, communication patterns, and individual contributions. By assessing these factors, team leaders can gain insights into the team’s performance and identify areas that need attention. Once weaknesses are identified, strategies can be implemented to improve team effectiveness and promote continuous growth. These strategies may include team-building activities, training programs to enhance skills, and fostering a culture of open communication and collaboration. Additionally, regular feedback and performance evaluations can help track progress and ensure continuous improvement in team performance. By continuously evaluating and improving various aspects of team performance, entrepreneurial teams can enhance their overall effectiveness and increase their chances of success.

Learning and Development: Nurturing Long-Term Success in Entrepreneurial Teams

In the context of entrepreneurial teams, continuous learning and professional development play a crucial role in nurturing long-term success. This subtopic explores the importance of ongoing learning and development opportunities for entrepreneurial teams.

Key points to consider include:

• Continuous learning enables team members to stay updated with industry trends and developments.
• Professional development programs provide opportunities for acquiring new skills and knowledge.
• Ongoing learning fosters innovation and adaptability within the team.
• Professional development initiatives enhance the team’s problem-solving abilities and decision-making skills.
• Nurturing a culture of continuous learning and professional development contributes to the long-term success of entrepreneurial teams.

Frequently Asked Questions

How can conflicts within an entrepreneurial team be effectively resolved.

Conflict within an entrepreneurial team can be effectively resolved through conflict resolution techniques, such as active listening, mediation, and compromise. Effective communication, including clear and open dialogue, is crucial in addressing conflicts and fostering a positive team environment.

What Traits Are Essential for Entrepreneurial Team Members to Be Adaptable and Open to Feedback?

Traits essential for entrepreneurial team members to be adaptable and open to feedback include a willingness to embrace change, flexibility in response to new information, humility to accept constructive criticism, and a growth mindset that views feedback as an opportunity for improvement.

How Does Teamwork in Entrepreneurship Contribute to Increased Creativity and Problem-Solving Abilities?

Increased collaboration in entrepreneurship fosters innovative thinking, leading to enhanced creativity and problem-solving abilities. Research shows that teams that effectively collaborate and leverage diverse perspectives are more likely to generate novel ideas and find innovative solutions to challenges.

What Strategies Can Be Used to Build a Successful Entrepreneurial Team?

Strategies for building a successful entrepreneurial team include building trust among team members, fostering effective communication, and ensuring clear roles and responsibilities. These factors contribute to a cohesive and productive working environment, enhancing the team’s overall performance.

How Does Diversity in Skills, Backgrounds, and Perspectives Contribute to the Success of an Entrepreneurial Team?

Diversity in skills, backgrounds, and perspectives contributes to the success of an entrepreneurial team by enabling synergy and collaboration. It allows for a wider range of ideas, problem-solving approaches, and innovation, resulting in enhanced team performance and outcomes.

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Transcript — August 28, 2024

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This transcript is from a CSIS event hosted on August 28.  Watch the full video here.

Kathleen J. McInnis: In the summer of 2020, Mellody Hobson was approached by her C-suite colleagues in search of a corporate solution to the nation’s demands for racial equity and justice that were sparked by the George Floyd protests. A force of nature on Wall Street as co-CEO and President of Ariel Investments, the nation’s first Black-owned asset management firm, Mellody recognized that the solution must be rooted in deep, systemic change. She put pen to paper and by February 2021 had created Ariel Alternatives, the first private equity subsidiary of the 40-year-old investment firm, alongside its current CEO, Les Brun.

Last year, Ariel Alternatives closed its inaugural Project Black fund at $1.45 billion, making it one of the largest private equity fund closings for a first-time manager in history. The fund’s goal? To scale sustainable minority owned businesses to serve as leading vendors to Fortune 500 companies, generating jobs and economic growth within underrepresented communities, and ultimately closing the racial wealth gap. Needless to say, as we get into her decision making when establishing Ariel Alternatives and crafting its unique investment thesis, we will learn a lot from Mellody about how to be both a creative and determined leader.

I’m your host, Dr. Kathleen McInnis, and this is Smart Women, Smart Power.

(Music plays.)

This is Smart Women, Smart Power, a podcast that features conversations with some of the world’s most powerful women.

(Music ends.)

Mellody, it is such an honor to have you here today. You – we’ve admired for years. You’re a member of the CSIS Board of Trustees. I’m just delighted that our audience is going to get to learn from you today.

Mellody Hobson: Thank you so much. I’m delighted to be here.

Dr. McInnis: Well, so I would love to start with your origin story. I think you are currently leading the company that you started at as an intern. Like, what grew you – drew you to this career in finance and kept you into this field?

Ms. Hobson: My story is, I think, the story of so many Americans, of the American dream, and what is possible, and not without great struggle and sacrifice and a tremendous work ethic. But I started off in Chicago. I’m the youngest of six kids in my family. My siblings always joked that I was not planned because I am more than 20 years younger than some of them. (Laughter.) And they made a point of joking with me about that. So in some ways, I’m an only child, because if you have more than five years between yourself and your siblings you’re an only child, and my closest sibling is nine years older than me.

So I grew up in Chicago to a single mom. My mom worked really, really hard. But despite the effort – I told the story many, many times – had a hard time sometimes keeping a roof over our heads, sometimes with food, and transportation to school. All of those things became very, very hard. And as a result of that, we would get evicted, our phone would get disconnected, our lights turned off – all sorts of things happened. It led to a very unstable childhood where I felt I had no control, as most children don’t. And I became very resolved about what I could control. And what I could control was my performance at school. And I thought if I did really, really well at school, I could have options.

And so ultimately, I got to go to Princeton – which was amazing. And I worked so hard for that for so many years. And while at Princeton, very early in my career – my freshman year – I had the opportunity to intern at Ariel Investments. And I was 19 years old. And I really learned investing – about investing for the first time. It was something I knew nothing about. I didn’t grow up in a home with money. I didn’t grow up in a home where the stock market was discussed. But I realized that there was a whole nother world. And that world made a lot of sense to me. It was a world that I wanted to learn more about.

I was desperate to understand money. I tell people that. Not to have a lot of it, I wanted to understand it. I thought, if I can understand it and understand how it works I won’t be in the perilous situations I had been in before as a child. And so in many ways, my purpose in life was born out of the financial security that I grew up in that ultimately led to my desire to have financial knowledge. And ultimately, once I realized that that knowledge could be so powerful and stabilizing, having a desire to pass that knowledge on to other people.

Dr. McInnis: Well, it feels like building economic opportunity for people to create better lives for themselves and the communities that they’re in is one of the major through lines of some of your work and the organizations you’ve established, which is incredible that, you know, making things better for people is such an important calling. And it brings us to the decision that you brought with us today, which is the founding of Ariel Alternatives, designed to invest in minority-owned businesses and close the racial wealth – I mean, just thinking about it in terms of the scale of the challenge. You don’t shy from big – (laughs) – shy away from big problems. So I guess, could you set the scene for us? What was happening at the time when the idea, the need for Ariel Alternatives was beginning to formulate, or beginning to bubble up?

Ms. Hobson: We were all locked in our homes in COVID. And I was doing conference calls sort of every other week with some very senior Black leaders in the country. And we were saying to ourselves, what is our role? What should we be doing right now? Where are there opportunities for us to make a difference in our community? We have a saying at Ariel, we’ve admired the problem long enough. We don’t admire problems. We act. And so during that summer it was also the summer of great social unrest because of the horrific murder of George Floyd, where many people were saying: We must do something about the racial inequity that exists in this country.

And so we said, what could we do here? And we started to think about the opportunities for affecting change. And we came up with something that was really white space, because we really were thinking in ways that people hadn’t thought before. One thing also that we were – as we were locked in our homes – I told our Ariel team, we are not going to limp out of COVID. We’re going to slingshot out of COVID. We’re going to be pulling that rubber band back and back, and we’re going to be warehousing ideas, and getting work done, and so when this is over we will pole vault ahead.

And so as we were sitting, and working, and thinking, this idea of Project Black was born. And it was the idea, could we scale sustainable minority businesses at a time when corporations were saying they were committed to giving more opportunity to people of color, both inside the organizations and in doing business with them? In hearing these pronouncements and announcements, we started to realize there was a true scale challenge when it comes to doing business with the Fortune 500 in corporate America. More specifically, 95 percent of minority businesses in this country have less than $5 million in revenue. Only five Black businesses in the United States have over a billion dollars in revenue. Five.

And so we said, OK, if you’re a giant Fortune 500 company and you want to do business with a minority company, you don’t want to write 100 separate $2 million purchase orders. You want to write

a $200 million purchase order. But we have a scale challenge. We don’t have businesses that are big enough to handle that opportunity. So we said, we want to think about this totally differently. When people think about minority businesses, they think small. We’re going big or going home. So we’re going to buy businesses, middle market, businesses that may not be minority owned when we buy them but through our ownership become what I called minoritized.

And through that minority ownership, we are able to become and be tier one suppliers to Fortune 500 companies that want to diversify their supply chain, both figuratively and literally – because during COVID, those undiversified supply chains caused lots and lots of problems. Said, we want to be there but we need to have the scale to do it. So writing bigger equity checks – very different than how people thought of minority businesses before, where they thought they’re going to grow these small businesses to scale, which takes decades. We said, we’re going to go right in the middle. We’re going to buy bigger businesses. And we’re going to grow them to be even bigger. But we’re going to do it in a rifle shot way. We will buy six to 10 platform businesses, and with the goal of over a decade creating a handful of billion-dollar Black and brown businesses.

Dr. McInnis: To dive a little bit more into your thought process and how you approach or developed this incredibly elegant solution, was it a flash of inspiration? Was it a team building thing? How did you – how did you come to this model?

Ms. Hobson: Iteration.

Dr. McInnis: Iteration.

Ms. Hobson: So I started with this idea of could we do private equity totally differently than had been done? One of the major features of what we do is something called demand aggregation, where we go to corporations and what we call the CPO, the purchasing officers of those – chief purchasing officers. We developed a council of Fortune 500 companies. And we said, if we – tell us what kind of businesses you need to be in your supply chain, and what kind of businesses that, if they were minority owned, would be particularly attractive to you. And so we did something called demand aggregation. Before we buy a business, we can get a sense of what kind of demand would be there for that product or service.

That is a really positive feature when you think about not knowing what could happen to a company. It gives you more certainty about it. Nothing is certain, but it certainly pushes you further on the – in the spectrum of being able to know what the potential is for the business. And so we really did see, as we were iterating, we were talking to people, I prepared a memo. And this memo was a result of Jamie Dimon calling me. Jamie called and said, during the middle of the pandemic, Mellody, a lot of people want to help Black businesses. So I’d been talking to all of these Black business leaders. And I said, Jamie, I think I have an idea.

I wrote a memo over the weekend. And in the spirit of investment banking, I gave it a pseudonym and I called it Project Black. (Laughter.) I delivered that memo to him on Monday. But before I delivered it to him, I sent it to the smartest people I knew and I said, shred this idea. Just destroy it. Tell me everything that’s wrong about it. Tell me how naive I am. And people came back with their feedback. They really took it seriously. I recrafted it. And by the time I sent it to Jamie, I felt really good about – I said, I think we’re on to something. And then he called back and he said, you’re on to something. And like to co-invest with you, to the extent that that might be possible.

Dr. McInnis: Wow. Has there been any particular success story over the course of Ariel Alternatives that’s really stuck with you so far?

Ms. Hobson: There are a few things that really stick out for me. First of all, the team that we’ve been able to amass. These are the best and brightest in the industry. And they happen to look like me and look like you. And that is something that is just heretofore, in the scale and the numbers that we have diversity represented at Ariel Alternatives – and it’s not all Black, or all women, but certainly we have a very large representation. Which is completely the opposite of what we’ve seen in most private equity firms, where there are few, if any, people that look like either one of us.

And so that is something – I remember being on a Zoom and we were pitching a CEO one day. And I literally said to them – all of our faces were on the – in the boxes on Zoom. And I welled up. And I said, oh my God, this is my dream. This is what I want – I’ve wanted to see my whole life of working at Ariel and all the things we’ve built, and making sure we all have a shot at this – narrowing this wealth gap, and putting our stamp on the industry and society. And I was looking at it. And that – with the best resumes, you know, like, the highest quality leaders you could possibly imagine that we had amassed. And I just took such great pride in that moment. That was before we had even done anything yet, just assembling the team. (Laughter.) So that was one that was meaningful.

Two, closing the fund. I mean, I remember the day. It was just such a big day. It happened to be the same day that I got to be on the cover of Forbes. And I remember just being so overwhelmed by the opportunity that we had at hand, that we had closed this $1.45 billion fund – first time – probably in the top five of first-time funds ever that had been closed. And it was, of course, based upon, again, a good idea that I think people expect us to execute well. So just that, that we could actually convince people in $100 million checks to support the concept. So that was a major milestone.

And then when we bought our first business. We bought a company called Sorenson Communications. Sorensen provides tech-enabled services to the deaf and hard of hearing. And when we bought that company I said, of course we would buy that business, a business that is directly related to those who are also disenfranchised, but where it’s a critical issue that, again, you could be a tier one supplier, best in class, to corporate America for both the people who work inside of their company that might be deaf or hard of hearing, but also, perhaps, the customers that they serve.

And so that, to me – we were able to, again, see where there was a need, and that we could own this business, and ultimately hopefully take this business to new heights. So it’s not to suggest in any way any of this has been easy. This is, like, I can’t even tell you – (laughter) – it’s like carrying this giant rock up a hill. And sometimes it does roll backwards. But also at the same time just feeling great purpose in the work, which is very fulfilling and gives me joy.

Dr. McInnis: Well, speaking of things you’re doing to change the world, you’re releasing a children’s book in October, “Priceless Facts About Money.” Can I just – why are you focused on financial literacy specifically? And what drove you to write a children’s book? By the way, writing any book and getting it out there is, like, a monumental accomplishment. So kudos.

Ms. Hobson: Well, this is the book. You know, it’s – it has not been released to the to the public yet, but this is one of the early copies. And it comes out in October. It’s called “Priceless Facts About Money.” OK, so, as my husband jokes, I was very busy during COVID. (Laughter.)

Dr. McInnis: Seems to be.

Ms. Hobson: He was, like, you should just lock yourself in the room regularly, because you got a lot done. (Laughter.) So I had this idea about a kid’s book, but I didn’t want the traditional – I would talk to publishers and they’re, like, who are the characters? You know, what’s the story? And

I’m like, no, that’s not what I’m talking about. And ultimately, I had my daughter who at the time was seven years old, and some friends who had children. I sent them all the most successful children’s books of all times – “Where the Wild Things Are,” “The Giving Tree.” You name it, I sent it to all these kids.

And I said, I want you to read these books. My daughter was just learning to read. And I want you to tell me what do you love about them? One child said something that just stuck with me. Austin Robinson (sp), who’s very close – the children of close friends. And he said: I love books about facts. And he’s like, I love nonfiction. And I’m, like, you know, and I’d been really resisting all these temptations of these – that had been put on me to – you know, or these recommendations that had been put on me to come up with a character that would teach kids about money. And I was like, no, it’s too sweet. It’s not what I – it’s not like I’m trying to hit kids with something that’s hard-nosed, but I want to be so realistic. And when he said that, it just flipped. And we’re going to write a book about amazing facts about money. And we’re going to teach kids about money from a factual basis, but the stories are going to be amazing.

And so we did. So we explained something, like, what is the first credit card? A Knight’s ring? The king or queen would give a knight a signet ring so that when they are moving around they would put their insignia in the bill that the innkeeper might have so that they didn’t get robbed when they were traveling. Then the innkeeper would take the bill to the palace, and that’s how they would get paid, with the insignia ring showing that it was a – the bill was good. So I said, this was literally the first credit card, when you think about that.

Dr. McInnis: (Laughs.) That’s fascinating.

Ms. Hobson: Yes, right? We do all of these things on, like, where do money – where do the names and the nicknames and the lingo for money come from? One, bucks. So people used to trade cattle, obviously. And there’s a line that I have in the book and says – it says, can you make change for a cow? No, right? So they started to trade the hides. And then the hides would get smaller and smaller, and ultimately ended up being bills. So that’s why they’re called bucks. So I give all of the examples. They are so good. I can’t even tell you. I mean, there are so many that are so fun.

Dr. McInnis: (Laughs.) I can’t wait to read this. This is awesome.

Ms. Hobson: You know, we talk about when is money a thing? And we do at, like, 100 million years ago, money’s not a thing. Fifty million years ago, money’s not a thing. And then I talk about when meteorites hit Earth and when dinosaurs die. And I’m, like, fossil fuels, you know, came to be in the Earth when the dinosaurs died. The meteorites are gold and silver and precious metals. So I start to explain how money becomes a thing. And just go through all of these things that, you know, most kids don’t think – when they think gold, oh, it was because of meteorite hit the Earth, and understand that that’s where it came from.

So these are the kind of things that we do. And it is – I mean, I had so much fun. I mean, I had researchers helping me. We would – we would focus on what were the best stories. Some I knew that I wanted to be in there, like, where did bull and bear come from? That was something I researched years and years ago, when I was trying to understand. There’s no really great true story on bull and bear, but the story that I like is it has to do with how they kill their prey. When a bull kills its prey it goes and pulls up with its horn, and when a bear kills its prey it runs and bears down on it. So bull markets, a stock market going up, bear markets, stock market going down.

So, again, lots of fun stories. We do currencies from around the world. Where do the symbols come from? We show you how the dollar sign came to exist. We show you how the euro came to exist. All of these things that you just wouldn’t think about.

Dr. McInnis: I cannot wait to read this book. And I know, like, my son, he’s two and a half, he loves fun facts. I mean, this is right up his alley. Thank you for putting this – this is fascinating. Oh, and so, but, working in the business world, you’ve been working to help our next generation understand financial literacy. Another major way that business leaders engage with building the world we want to see is through philanthropy. And wondering, like, as a leader in the – in the financial world, what areas do you think needs more attention or investment in, in the United States? What’s bothering you? What are you seeing that that needs to be worked on, from a philanthropic perspective?

Ms. Hobson: So much bothers me.

Dr. McInnis: OK, fair. (Laughs.)

Ms. Hobson: But there’s – you know, how do you eat an elephant? In small bites. You start with where you can. So I try to move the needle in areas where I have expertise. I think financial literacy is critical. I talk about that in the book. In the forward, I talk about the fact that money is the one thing that is universal. No matter where you – it’s sort of, like, you know, these people say death and taxes. But it’s true, money is one of those. You could be in an African village and you’ve got the issue with the cattle, or you could be in a major developed market, like, you know, America, or Hong Kong, or, I mean, China.

Whatever you want to say to show that, you know, no matter who you are – literally from CEO to schoolteacher to bus driver to fireman to doctor, lawyer, nurse – you have to deal with money. So because of that, money should be taught in schools in America. And it is not, which is shocking to me. And I give the example every time, in high school in America today you can take woodshop or auto, and not a class on investing. And it always leads me to ask audiences the same question: Who is whittling in their spare time?

Dr. McInnis: (Laughs.)

Ms. Hobson: Is cleaning their carburetor?

Dr. McInnis: Right.

Ms. Hobson: No one. And yet, this issue of money – your 401(k) plan, saving for your children’s education, saving for your retirement – we’re winging it, which makes no sense to me. And you know, home ec is – you know, teaches you how to read a utility bill; that’s not exactly helpful.

Dr. McInnis: Right. Well, and it also creates a lot of anxiety, right, for people who don’t have financial literacy. How do you approach this world and how do you – how do you get into it? How do you make wise decisions? How do you not lose everything?

Ms. Hobson: Well, one of the things we should know is that finances do cause anxiety for lots of people, rich or not rich.

Dr. McInnis: Yeah. Sure.

Ms. Hobson: The other thing is that money habits are learned; they’re not taught. You watch your parents, generally, or whoever your caretaker is, and how they deal with money, and it becomes hardwired in you.

Ms. Hobson: So parents that are always overextended or maxing out credit cards, et cetera, you are likely to grow up and ultimately do the same thing. Parents tell me all the time about their children when they tell them they can’t afford it and they say put it on a credit card. That’s because they do not know that it is money.

And when you think about it, the – which is also what we talk about in the book – the illusive nature of money for a child is something that must be really addressed.

Dr. McInnis: Yeah.

Ms. Hobson: They watch money come out of a machine in terms of an ATM.

Ms. Hobson: They see parents pay for things with credit cards or phones. And so it doesn’t have the – the idea that it has a finality to it and you run out becomes very hard for a child to understand.

Dr. McInnis: Absolutely.

Well, switching gears a bit, one of the things that has been kicked around in a lot of international strategic and other circles is this notion of polycrisis, right; like, that there’s multiple simultaneous crises and our governments, our societies, our businesses are not quite positioned to be able to grapple with all of this at the same time. So as a leading figure in the business and finance world, I’m curious as to your views as to, what do you think we should be focusing on? Or are there any things that you – any issues, any emerging developments that you wish that we were – we as a country, we as Washington – were more focused on?

Ms. Hobson: I wrote about this in our first quarter client letter, actually, the concept of polycrisis, and I talked about the fact that my belief is that we’ve all become firefighters.

Dr. McInnis: Yes.

Ms. Hobson: And it’s mindboggling because I can think about the financial crisis in ’08 that just seemed like, again, world on fire, U.S. on fire, especially when you’re in the investment business.

Ms. Hobson: You know, behemoths falling – Lehman Brothers, Bear Stearns, et cetera – something you could never imagine. Then you get to the COVID crisis and you’re like, wait a minute, the world is shut down and there are no cars on the street. Then, you know, you get – I could just keep going. Then you wake up and we’re in a couple of wars at the same time.

Ms. Hobson: You know, this is like pile on after pile on, all so tragic, so devastating in so many ways. Nothing about it is where you can feel like you can get your footing.

Ms. Hobson: And I think that that has destabilized people and created, obviously, tremendous anxiety, none more than the people who are actually living in warzone – war-torn areas. So, again, not to diminish that in any way. And, obviously, how climate has also factored into refugees, migrants, et cetera, around the world, not just in terms of America.

So we have a lot that is going on in this world. I think it is overwhelming, and I think that we have to start to recognize clearly – we have to have leaders who can handle this.

Ms. Hobson: We also have to have leaders who can keep cool heads, be practical, and be thoughtful about how to untangle ourselves as opposed to escalating some of these dramas and these tragedies that are occurring.

I think we all want a world that is one with peace. We do. And I know that’s easier said than done. You know, it’s easier to be a Monday morning quarterback sitting here saying you should do this, you should do that.

Ms. Hobson: I would not be so presumptuous to think that I could be, you know, second guessing some of the smartest minds in the world. But I would say I think it’s helpful when you have a goal, and the goal is you’re working towards something that’s very clear. I think that’s true of business, that’s true of growing up, that’s true of education, whatever it might be. And then when you’re working towards that goal, sometimes working even backwards from it, how do I get to that goal, being very clear about it, not admiring the problem as I said before – so many people sit around and navel-gaze and talk about why things are bad – what do you do? That old line: What trees do you plant?

Ms. Hobson: I think that’s very, very important because this is not every – this is not other people’s problem; it’s our problem. And the one thing that I think I’ve tried to demonstrate thorough either Ariel Alternatives or “Priceless Facts about Money” or the day-to-day life that I lead at Ariel is we’re not going to complain; we’re going to act. And if each person acts, we get something done.

Lastly, I once heard Bono, who I admire tremendously, say one day he feels like we’re all going to – we’re going to say that we were all standing around, the world was on fire, and everyone had a can of water, and if we all just threw the can into the fire –

Ms. Hobson: – the fire would go out. But we all have to recognize we’re holding the can of water.

Dr. McInnis: Wow. And I love the trees we plant. The trees we plant.

I’m wondering, do you feel that your gender as a woman has had an impact on how you’ve approached these problems, how you think about these problems, and the way you’ve led?

Ms. Hobson: Yes, for sure. I mean, I think that as a woman leader I think there are just different sensibilities. And I don’t think that one is right or wrong; they’re just different. I tell people you have morning people and night people. You know, one is not better than the other; they’re just different.

Ms. Hobson: They call them owls and larks. I read a book about that.

Ms. Hobson: I’m a – I’m a – I am a lark, so I’m up very early in the morning. But there is – there is – I think that gender does make a difference. I think for me, I am OK being vulnerable. I’m OK – you know, sometimes I cry in front of people.

Dr. McInnis: Shock. Shock, horror! No, that’s true. (Laughs.) Yeah, yeah.

Ms. Hobson: I remember being in a meeting once and I was having sort of a contentious conversation with someone, and I remember – in front of a group of people – and they did something that I don’t think they would have done if I weren’t a woman. They said: Mellody, we’re not leaving this meeting like this; give me a hug.

Dr. McInnis: Wow.

Ms. Hobson: And they gave me a hug in front of everyone.

Ms. Hobson: And I just thought that that was a really – it was a – it was a profound moment for me to think about how I could use my gender also to deescalate the situation. Not to be soft.

Ms. Hobson: I could be strong and not tough. I could be kind without being soft.

Ms. Hobson: But in that moment, that olive branch of kindness was actually one that became a physical hug, and I think it taught me and the room a lot. And I said: You know what? I think this is an advantage.

And to close out our conversation today, which has been absolutely fascinating, I would be curious as to your views on what is power. What does power mean to you? We’re Smart Women, Smart Power, so, yeah, how do you define it? How do you think about it?

Ms. Hobson: I think people think of power as being money or fame or fortune, and I think that that is wrong. I think people have power in every walk of life every single day. They choose to use it or not.

And the example that I give, which is my favorite example – because a lot of people say to me, well, you have power; you’re a co-CEO and you’re on these boards and, you know, you have resources, et cetera. I’m like, I just go back to Rosa Parks. She decided not to stand up. She had no obvious power. She had no obvious influence. And yet, she changed the trajectory of the civil rights movement, gave me the opportunity to sit in this seat doing what I do because she used the power that she had. She used her power for good.

I give one last example. I swim, and for years I swam with a swim coach, and my swim coach used to make me put something called fistgloves on, which are latex mittens that put your hands into fists. And you don’t use your – you don’t get to use your hands.

Dr. McInnis: Oh.

Ms. Hobson: So we do half the lesson with these fistgloves on, and it lets you see what’s wrong with your stroke, all sorts of things. And then halfway through the lesson he says: Take your gloves off, Mellody, but use your power for good. He’s giving me my hands back. Use your power for good. And I have never – I’ve used that analogy in all things in my life, something as simple as getting my hands back, using my powers for good in the water but also day-to-day life using your power for good no matter who you are.

Dr. McInnis: Mellody, thank you so much for this really rich and inspiring conversation. Thank you for being on Smart Women, Smart Power.

Ms. Hobson: Thank you for having me.

 (Music.)

 (END.)

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