Shortcuts to Multiply Decimals by 10, 100, or 1000

There are shortcuts that everyone can use when multiplying a number by 10, 100, 1000 or 10,000 and beyond. These shortcuts are referred to as moving the decimals. It is preferable that you first work to understand the multiplication of decimals prior to using this method.

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Multiply by 10s Using This Shortcut

To multiply by 10, you simply move the decimal point one place to the right. Let's try a few:

3.5 x 10 = 35 (We took the decimal point and moved it to the right of the 5.)
2.6 x 10 = 26 (We took the decimal point and moved it to the right of the 6.)
9.2 x 10 = 92 (We took the decimal point and moved it to the right of the 2.)

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Multiply by 100s Using This Shortcut

Now let's try multiplying 100 with decimal numbers. To do this means we will need to move the decimal point 2 places to the right:

4.5 x 100 = 450 (Remember, to move the decimal 2 places to the right means we also have to add 0 as a placeholder which gives us the answer of 450.)
2.6 x 100 = 260 (We took the decimal point and moved it two places to the right but needed to add 0 as a placeholder.)
9.2 x 100 = 920 (Again, we take the decimal point and move it two places to the right but need to add a 0 as a placeholder.)

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Multiply by 1000s Using This Shortcut

Now let's try multiplying 1000 with decimal numbers. Do you see the pattern yet? If you do, you will know that we need to move the decimal point 3 places to the right when multiply by 1000. Let's try a few:

3.5 x 1000 = 3500 (This time in order to move the decimal 3 places to the right, we need to add two 0s as placeholders.)
2.6 x 1000 = 2600 (To move three places, we need to add two zeros.)
9.2 x 1000 - 9200 (Again, we add two zeros as placeholders in order to move the decimal point 3 points.)

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Powers of Ten

As you practice multiplying decimals with the powers of ten (10, 100, 1000, 10,000, 100,000...) you will soon become very familiar with the pattern and you will soon be calculating this type of multiplication mentally. This also comes in handy when you use estimation. For instance, if the number you are multiplying is 989, you will round up to 1000 and estimate.

Working with numbers like these are referred to as using the powers of ten. The powers of ten and the shortcuts of moving decimals work both with multiplication and division, however, the direction will change based on the operation being used.