Multiply decimals by 10 100 1000
for 6th grade

Multiply decimals by 10 100 1000

Due to the fact that our number system is base 10, multiplying decimal numbers by powers of 10 is relatively simple. The digits of the number move around, and there are maybe zeros to add or remove, but the other digits all stay the same. Remember that when we multiply numbers by any number greater than 1 they get bigger so check this once your done.

Let's get our terms straight.

factor x factor = product

23.45 x 100   = 2345

So for the sum 23.45 x 100 = 2345,

• 23.45 and 100 are the factors
• 2345 is the product

When we multiply by 10 the product is 10x bigger than the initial factor.
When we multiply by 1000 the product is 1000x bigger than the factor.

Note that in the example above, the decimal point of the product is not written down because the product is an integer.

Multiply decimals by 10, 100 or 1000 : move the digits

Write the digital factor to be multiplied by a power of 10 down. Keep the digital point still and move all the digits of the digital factor to the left around it. If we are multipling by 10, all the digits move 1 column to the left. If we are multipling by 100, all the digits will move 2 columns to the left, and for multipling by 1000, it is 3 columns.

7.438 x 10 = 74.38

7.438 x 100 = 743.8

7.438 x 1000 = 7438

Alternative method : move the point

Another method is to keep the digits of the decimal number static and move the decimal point to the right. If the factor is 100 move it two places to the right, one for each of the zeros in 100. If you are not writing numbers down, this can be an easier method to visualise in your head.

0.0671 x 10 = 0.671

0.0671 x 100 = 6.71

0.0671 x 1000 = 67.1

Check your answer

Multiplying by a number greater than 1? Then product should be bigger than the original number!
Remember too that multiplying and dividing are inverse operations so you can always check a multiplication by dividing the product by whatever power of 10 you multiplied by and make sure you get the original value returned.

0.0671 x 100 = 6.71

6.71 ÷ 100 = 0.0671