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Dividing a decimal by a power of 10: pattern

Discover a pattern when dividing by powers of 10. Created by Sal Khan.

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Video transcript

In the last video, we divided 100 into 99.061, and we did it the manual way. We did it the long division way. In this video, I just want to show you a quick shortcut because we're dividing something by a power of ten. If I have 99.061, if I multiply by a power of ten, I'm going to make the number bigger. Every time I multiply by 10, the decimal would shift to the right by one spot. So we could say, 99.061 times 10 is going to be equal to 990.61. Notice we just moved the decimal over to the right by one. If I were to do-- I'll just arbitrarily switch colors-- 99.061 divided by 10, we're going to shift the decimal in the other direction. This is going to be 9.9061. So when we divide by 100, we're dividing by 10 twice. We're shifting to the left twice. So if we start with 99.061 divided by 100-- let me just write it like this. We've already written the problem. If we want to divide this by 100, moving it one spot to the left will divide it by 10, and then moving another spot to the left will divide it by 10 again. So 99.061 divided by 100 is going to be equal to 0.99061. We're just going to shift the decimal to the left by two. And we might want to put a leading zero here, just so it makes it a little bit easier to read.