Multiplying Decimals

We have just begun to talk about what happens to a number when it is multiplied by 10, 100, 1,000, .1, .01, and .001.

For example, when 9 is multiplied by the numbers, you would see:

9 x 10 = 90
9 x 100 = 900
9 x 1,000= 9,000
9 x .1 = .9
9 x .01 = .09
9 x .001 = .009

This shows us that a number multiplied by a 10 will get larger by one place value (9 was a ones but when multiplied by 10, it becomes 90 (or a tens)) and each multiple of ten causes the whole number to grow by that many place values (9 x 100 will grow two place values, 9 x 1,000 will grow by 3 place values, etc...)

On the other hand, if a number is multiplied by a decimal number, then the number will decrease by that number of place values (9 multiplied by .1 will go from a 9 (which is in the ones) to a .9 (which is in the tenths place value) and each time the decimal increases, the number will get smaller than number of place values (9 x .01 will go back two place values, 9 x .001 will go back 3 place values).

More Examples:

3.25 x 1,000 = 3,250
3.25 x 100 = 325
3.25 x 10 = 32.5
3.25 x 1 = 3.25
3.25 x .1 = .325
3.25 x .01 = .0325
3.25 x .001 = .003

.4 x 1,000 = 400
.4 x 100 = 40
.4 x 10 = 4
.4 x 1 = .4
.4 x .1 = .04
.4 x .01 = .004
.4 x .001 = .0004

When multiplied by a whole number, the decimal moves to the right making the number larger; however, when multiplied by a decimal number, the decimal moves to the left making the number smaller in value.