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Fractions as division by power of 10

Explore the concept of multiplying and dividing numbers by powers of 10. Understand how moving the decimal point to the left or right changes the value of a number, and how this relates to the concept of fractions as division. Created by Sal Khan.

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Video transcript

So I have six different fractions written out here, and what I want you to do is pause this video right now and try to rewrite each of these fractions as a decimal. So I'm assuming you've given a go at it, so let's go through each of these. So we know that when we say 34/10, or 34 over 10, that this could be interpreted literally as 34 divided by 10. And so if you start with 34-- let me put a little decimal right over here. It will be clear that there is an implied decimal there, so we could just keep adding zeroes if we want. So when we divide by 10, we're going to move the decimal one space over to the left. And you should always do a reality check. If you forget, hey, do I move it over to the left, or do I do it over to the right? You should do a reality check. Look, if I'm dividing by 10, should I get a smaller value or a larger value? Well, clearly, if you're dividing it into 10 groups, you should get a smaller value. So when you take your decimal place to the left, you're going to get a smaller value. 34 is going to become 3.4. And that makes complete sense. If you were to multiply 3.4 by 10, you would move the decimal to the right, and you would get to 34. Let's think about this one. So this one right over here is 3.4. Now let's think about 7/10. So the exact same idea. This is equal to 7 divided by 10. This fraction, horizontal line symbol thing could literally be viewed as "divided by." This could be read as 7 divided by 10. So when you divide by 10, you move the decimal one space over to the left. So we're going to get to point 7. And just to be clear, we could write this as 0.7. It's sometimes dangerous to just write the decimal without the zero out front. So 7/10, or 7 divided by 10, can be rewritten as 0.7. Now let's try 53/100. Well, we'll start with our 53. Once again, this could be interpreted as 53 divided by 100. So there's an implied decimal point right over here. Now, if we're dividing by 100, that's dividing by 10 and then dividing by 10 again. This is dividing by 10 times 10. So we're going to divide by 10, and then we're going to divide by 100. So the decimal is going to land right over there. So that's going to get us to 0.53. Now let's tackle 2 divided by 100. So once again, this could be rewritten as 2 divided by 100. 2/100 is the same thing as 2 divided by 100. If we start with a 2, put our decimal point right there. So we're going to divide by 10, and we're going to do that twice. So we're going to divide by 10 once. That would be 2/10. That puts our decimal there. But we have to divide by 10 again. You might say, hey, look, there's nothing here. Well, you could just throw a zero on here, just so that you do something there, and then you have moved your decimal over to the left twice. Remember, every time you're doing it, you're dividing by 10. You're dividing by 10. Then you're dividing by 10 again. Dividing by 10 two times, that's the same thing as dividing by 100, because 10 times 10 is 100. So this is going to be 0.02. Now we've already seen that, if you were to try to read this, this 2 is in the hundredths place. So you would literally read this as 2 hundredths. And we see that right over here. We've literally represented it as 2 hundredths right over there-- 2/100. So now we have 1,098 divided by 100. Well, same drill. Or 1,098 hundredths I could say. That's the same thing as 1,098 divided by 100. So we could start with 1,098. The decimal is implicitly right over here, but we need to move it two spaces to the left-- one, two-- because we're dividing by 100. That gets us to 10.98. And always do a reality check. Look, it makes sense. We got to a significantly smaller value when we divided by 100. Now we'll just divide 9,967 by 1,000. Well, 9.967, decimal point implicitly there. Now, 1,000 is 10 times 10 times 10. So if you're dividing by 1,000, that's dividing by 10 three times. So we'll divide by 10 once, divide by 10 twice, divide by 10 three times. We get to 9.967. So another way of writing 9,967 thousandths, well, that's just going to be 9.967. Or I could literally read it as 9 and 967 thousands. And that also makes sense. I mean, you could break this up into 9,000 plus 967. And so 9,000 thousandths is going to be 9. And then you're going to be left with the 967 thousandths.