## Multiplication by Powers of 10

Multiplying by ten's may be computed quickly by noticing the following pattern:

10 x 10 = 100

100 x 10 = 1000 (= 10 x 10 x 10)

1000 x 10 = 10,000 (= 10 x 10 x 10 x 10)

10,000 x 10 = 100,000 (= 10 x 10 x 10 x 10 x 10)

It follows that the number of zeros in each each product equals the number of times 10 was used as a factor. This product is known as the power of 10. As an example:

10,000,000

has seven 0's and equals 10 x 10 x 10 x 10 x 10 x 10 x 10

When multiplying a number by a power of 10, the result may be determined by moving the decimal place to the right by the same number of zeros in the power of 10 and inserting 0's into any empty places.

Example #1:

3149.625,832,119,333 x 1000 = ?

Solution #1:

As 1000 contains three 0's, the answer
may be determined by moving the decimal three places to the right and inserting 0's into
those empty places:

5,832,119,333,000

Example #2:

0.314962 x 10,000 = ?

Solution #2:

As 10,000 contains four 0's, the answer may be determined by moving the decimal four places to the right (no empty places to fill with 0's):

As 10,000 contains four 0's, the answer may be determined by moving the decimal four places to the right (no empty places to fill with 0's):