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
×10
| Move the decimal point one place to the right.
|
×100
| Move the decimal point two places to the right.
|
×1000
| Move the decimal point three places to the right.
|
Example 1
Calculate 2.25×1000.
Identify the multiplier.
2.25×1000
Move the decimal point three places to the right.
2.25↷
2.250↷↷
2.2500↷↷↷
Complete the multiplication.
2.25×1000=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
÷10
| Move the decimal point one place to the left.
|
÷100
| Move the decimal point two places to the left.
|
÷1000
| Move the decimal point three places to the left. |
Example 2
Calculate 422.5÷100.
Identify the number you are dividing by.
422.5÷100
Move the decimal point two places to the left.
422↶.5
422↶↶.5
Complete the division.
422.5÷100=4.225
Note: Only the decimal point moves position when dividing by 10,100,1000.