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Multiplying and dividing decimals by 10, 100 and 1000

Tutor: Labib

# Multiplying and dividing decimals by 10, 100 and 1000

## ​​In a nutshell

Decimal numbers are numbers with digits which are not zero after a decimal point. To multiply or divide decimals by $10,100,1000,$ you must use place values to move the decimal place a certain number of places to the left or right.

## Multiplying decimals by 10, 100, 1000

To multiply decimals by $10,100,1000$​, follow this procedure:

#### PROCEDURE

 ​​​​$\times10$​​ Move the decimal point one place to the right. ​$\times 100$​​ ​Move the decimal point two places to the right. ​$\times 1000$​​ ​Move the decimal point three places to the right.

##### Example 1

Calculate $2.25 \times 1000$​.

Identify the multiplier.

$2.25 \times \underline{1000}$​

Move the decimal point three places to the right.

$2.\overset{\curvearrowright\,\,\,\,\,}{2\thinspace 5 \thinspace}$​​

$2.\overset{\curvearrowright\,\curvearrowright\,\,\,\,}{2\thinspace 5 \thinspace 0}$​​

$2.\overset{\curvearrowright\curvearrowright\curvearrowright\,\,\,}{2\thinspace 5 \thinspace 0\thinspace0}$

Complete the multiplication.

$\underline{ 2.25 \times 1000 = 2250.0 = 2250}$​​

Note: $0$ is a placeholder which is used if you reach the end of a decimal number. If a $0$ is at the very end of a decimal it can be removed from the final answer.

## Dividing decimals by 10, 100, 1000

To divide decimals by $10,100,1000$​, follow this procedure:

#### PROCEDURE

 ​​​​$\div10$​​ Move the decimal point one place to the left. ​$\div100$​​ ​Move the decimal point two places to the left. ​$\div1000$​​ ​Move the decimal point three places to the left.

##### Example 2

Calculate $422.5 \div100$

Identify the number you are dividing by.

$422.5 \div \underline{100}$​

Move the decimal point two places to the left.

$42\overset{ \curvearrowleft}{2\thinspace }.5$​​

$4\overset{\curvearrowleft \curvearrowleft}{2\thinspace 2 }.5$​​

Complete the division.

$\underline{422.5 \div 100 = 4.225}$

Note: Only the decimal point moves position when dividing by $10,100,1000$.​

## FAQs - Frequently Asked Questions

### What is a decimal?

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