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# Multiply a Decimal by 10, 100, 1000, or 10,000

Multiply a Decimal by 10, 100 or 1000 Worksheets
There are shortcuts that we all use when multiplying a number by 10, 100, 1000 or 10,000 and beyond. We refer to these short cuts as moving the decimals. I do recommend that you work to understand multiplication of decimals prior to using this method.

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)

Now lets 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 moe it two places to the right but need to add a 0 as a placeholder)

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.

As you practice multiplying decimals with the powers of ten (10, 100, 1000, 10,000, 100,000...) you will soon become very familar with the pattern and you will soon be calculating this type of multiplication mentally. This also comes in handy when you use estimation. For intance, 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 changed based on the operation being used.

Now you are ready to try a few worksheets:
Multiply 2 and 3 digit numbers by 1000.
Multiply 2 and 3 digit numbers by 10, 100, 1000 and 100,000

Deb Russell