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Lesson 65: Multiplying and Dividing by Powers of 10
This lesson shows you some easy shortcuts for the times that you need to multiply or divide by a power of 10, such as 10, 100, 1000, etc.
Recall from Lesson 62 that powers of 10 are 10, 100, 1000, etc. There is an easy shortcut for when you need to multiply by a power of 10. Just take the number you are multiplying, and on its right of the number of zeroes that is in the power of 10 that you are multiplying it by.
For example, to multiply 48 x 10, just add one zero on its right to get 480. To multiply 48 x 100, just add two zeroes on its right to get 4,800, and so on.
If the number has a decimal point, just move the decimal point
one space to the right for every zero in the power of 10 that you
are multiplying by. For example, to multiply
4.278 x 10, just move the decimal point one space to the right to
get 42.78. To multiply 4.278 x 100, just move the decimal
point two spaces to the right to get 427.8, and so on.
If you want to divide a number by a power of 10, just do the exact opposite of everything described above. For example, to do 5700 ÷ 10, just drop a zero from the right to get 570. To do 5700 ÷ 100, drop two zeros to get 57.
If the number has a decimal point, just move the decimal point
two spaces to the left for every zero in the power of 10 that you
are multiplying by. For example, to do
254.7 ÷ 10, move the decimal one place to the left to get 25.47.
Remember that if a number doesn't have a decimal, such as 93, you
can rewrite it as 93.0, which is the equivalent. Then move
that decimal point as many places to the left as you need to.
Note that you might need to add extra zeros on the left. For example, to do 9.27 ÷ 100, you have to first add a zero on the left of that number so that when you move the decimal point two places to the left, you will get .0927. It's best to write that as 0.0927 so that it is easy to see where the decimal point is.
Multiplying and dividing by powers of ten comes up quite a bit in math class, and also in everyday life. Memorizing these shortcuts will help save you quite a bit of time.
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