What is a power of 10?

A power of 10 refers to numbers such as: 10, 100, 1000 etc.

How do you divide by a power of 10?

Count how many zeros are in the power of 10, and move the decimal point to the left by the same amount.

How do you multiply by a power of 10?

Count how many zeros are in the power of 10, and move the decimal point to the right by the same amount.

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Chapter overview

Learning goals

Maths

Multiplying and dividing by powers of 10

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Summary

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Multiplying and dividing by powers of 10

In a nutshell

Powers of 10 refer to 10, 100, 1000 and so on. To multiply and divide by powers of 10, you have to use place values to move the decimal place a certain number of steps to the left or right.

Multiplying by powers of 10

To multiply by powers of 10, follow this procedure:

procedure

1.	Count how many zeros there are in the power of 10.
2.	Move the decimal point to the right by the same amount.

Note: If the number is a whole number, then add " $.000...$ ", adding as many zeros as required.

Example 1

What is $3.2\times1000$ ?

First, count how many zeros are in $1000$ . Then, write $3.2$ as $3.2000..$ and move the decimal point $\textbf{3}$ places to the right. Finally, get rid of the extra zeros past the decimal point.

Dividing by powers of 10

To divide by powers of 10, it is exactly the same as multiplying, except the decimal point moves the other way.

procedure

1.	Count how many zeros there are in the power of 10.
2.	Move the decimal point to the left by the same amount, adding zeros to the left if necessary.

Example 2

What is $25\div100000$ ?

First, count how many zeros there are in $100000$ . Then, write $25$ as $...000025.0$ , and move the decimal point 5 places to the left. Get rid of the unnecessary zeros.

Multiplying and dividing by multiples of powers of 10

Multiples of powers of 10 refers to numbers such as: 30000, 20, 800 and so on. To multiply and divide by these numbers, first you have to multiply or divide by the multiple (the number "attached" to the power of 10).

Example 3

What is $400\div50000$ ?

First, write $50000$ as $5\times10000$ .

To compute $400\div50000$ , first do $400\div5$ and then divide the answer by $10000$ , using the method above:

$400\div5=80$

$80\div10000=0.\overset{\curvearrowleft \curvearrowleft \curvearrowleft \curvearrowleft}{0\thinspace 0\thinspace 8\thinspace 0}$

$80\div10000=0.008$

$\underline{400\div50000=0.008}$

Multiplying and dividing by powers of 10

In a nutshell

Powers of 10 refer to 10, 100, 1000 and so on. To multiply and divide by powers of 10, you have to use place values to move the decimal place a certain number of steps to the left or right.

Multiplying by powers of 10

To multiply by powers of 10, follow this procedure:

procedure

1.	Count how many zeros there are in the power of 10.
2.	Move the decimal point to the right by the same amount.

Note: If the number is a whole number, then add " $.000...$ ", adding as many zeros as required.

Example 1

What is $3.2\times1000$ ?

Dividing by powers of 10

To divide by powers of 10, it is exactly the same as multiplying, except the decimal point moves the other way.

procedure

1.	Count how many zeros there are in the power of 10.
2.	Move the decimal point to the left by the same amount, adding zeros to the left if necessary.

Example 2

What is $25\div100000$ ?

First, count how many zeros there are in $100000$ . Then, write $25$ as $...000025.0$ , and move the decimal point 5 places to the left. Get rid of the unnecessary zeros.

Multiplying and dividing by multiples of powers of 10

Example 3

What is $400\div50000$ ?

First, write $50000$ as $5\times10000$ .

To compute $400\div50000$ , first do $400\div5$ and then divide the answer by $10000$ , using the method above:

$400\div5=80$

$80\div10000=0.\overset{\curvearrowleft \curvearrowleft \curvearrowleft \curvearrowleft}{0\thinspace 0\thinspace 8\thinspace 0}$

$80\div10000=0.008$

$\underline{400\div50000=0.008}$

Want to find out more? Check out these other lessons!

Multiplying and dividing decimals by 10, 100 and 1000

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Frequently Asked Questions (FAQ)

FAQs

Question: What is a power of 10?

Answer: A power of 10 refers to numbers such as: 10, 100, 1000 etc.
Question: How do you divide by a power of 10?

Answer: Count how many zeros are in the power of 10, and move the decimal point to the left by the same amount.
Question: How do you multiply by a power of 10?

Answer: Count how many zeros are in the power of 10, and move the decimal point to the right by the same amount.

Theory

Exercises

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Multiplying and dividing by powers of 10

Multiplying and dividing by powers of 10

​​In a nutshell

Multiplying by powers of 10

procedure

Example 1

Dividing by powers of 10

procedure

Example 2

Multiplying and dividing by multiples of powers of 10

Example 3

Multiplying and dividing by powers of 10

​​In a nutshell

Multiplying by powers of 10

procedure

Example 1

Dividing by powers of 10

procedure

Example 2

Multiplying and dividing by multiples of powers of 10

Example 3

Want to find out more? Check out these other lessons!

Now you’ve read the summary, have a go at the exercises!

In a nutshell

In a nutshell