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 $10,100,1000$ .