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

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

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 $$10,100,1000$$.​