How to multiply decimals by 10, 100 and 1000

A quick guide to multiplying decimals by powers of ten

The modern way of teaching this topic is to get you to move the entire number either one, two or three places to the left in a place value table. While I love place value tables and find them very useful, I feel that there is an easier way of looking at the whole multiplying decimals thing.

The method I use (which I was taught in school, several decades ago) is to move the decimal point to the right.


To multiply a decimal by 10, you move the decimal point one place to the right.

For example:

123.42 x 10 = 1234.2

and

22.9 x 10 = 229

(This idea works even when you’re multiplying whole numbers rather than decimals. For example, you know that 48 x 10 = 480. You could think of the 48 as 48.0, and move the decimal point one place to get your answer of 480.)



To multiply a decimal by 100, you move the decimal point two places to the right.

For example:

242.867 x 100 = 24,286.7

Supposing you have a calculation like 8.7 x 100. You might think that there aren’t enough places to move the decimal point. However, you can simply add a couple of zeros after the 7, and then do the calculation:

8.700 x 100 = 870.0 = 870



To multiply a decimal by 1000, you move the decimal point three places to the right.

For example:

26.679 x 1000 = 26,679

and

9.02 x 1000 = 9.0200 x 1000 = 9020.0 = 9020

© Empress Felicity May 2012

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