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Multiplying and dividing by powers of 10

Tutor: Bilal

# 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 zeroes 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:

$400\div5=80$​​

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

$80\div10000=0.008$​​

$\underline{400\div50000=0.008}$​​

## FAQs - Frequently Asked Questions

### How do you multiply by a power of 10?

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