Topic B: Foundations
Dividing a decimal by a power of 10
We're asked to divide 99.061, or 99 and 61/1000, by 100. And there's a few ways to do it. But what I want to do in this video is focus on kind of a faster way to think about it. And hopefully it'll make sense to you. And that's also the focus of it, that it makes sense to you. So 99, let's just think about it a little bit. So if we-- so 99.061. So if we were to divide this by 10, just to make the point clear, if we were to divide this by 10, what would we get? Well, we would essentially move the decimal place one spot to the left. And it should make sense because we have a little over 99. If you took 99 divided by 10, you should have a little over 9. So essentially, you would move the decimal place one to the left when you divide by 10. So this would be equal to 9.9061. If you were to divide it by 100, which is actually the focus of this problem, so if we divide 99.061 divided by 100, if we move the decimal place once to the left, we're dividing by 10. To divide it by 100, we have to divide by 10 again. So we move it over twice. So one, two times. And so now the decimal place is out in front of that first leading 9, which also should make sense. 99 is almost 100, or a little bit less than 100. So if you divide it by 100, we should be a little bit less than 1. And so if you move the decimal place two places over to the left, because we're really dividing by 10 twice, if you want to think of it that way, we will get the decimal in front of the 99-- 0.99061. We should put a zero out here. Just sometimes it clarifies things. So then we get this right over here. Now, one way to think about it, although I do want you to always imagine that when you move the decimal place over to the left, you really are dividing by 10 when you move it to the left. When you move it to the right, you're multiplying by 10. Sometimes people say, hey, look, you could just count the number of zeroes. And if you're dividing, so over here, you were dividing by 100. 100 has two zeroes, and we're dividing by it, so we could move our decimal two spaces to the left. That's all right to do that, especially it's kind of a fast way to do it. If this had 20 zeroes, you would immediately say, OK, let's move the decimal 20 places to the left. But I really want you to think about why that's working, why that makes sense, why it's giving you a number that seems to be the right kind of size number, why it makes sense that if you take something that's almost 100 and divide by 100, you'll get something that's almost 1. And that part, frankly, is just a really good reality check to make sure you're going in the right direction with the decimal. Because if you tried this 5, 10 years from now, maybe your memory of the rule or whatever you want to call it for doing it, you're like hey, wait, do I move the decimal to the left or the right? It's really good to do that reality check to say, OK, look, If I'm dividing by 100, I should be getting a smaller value and moving the decimal to the left gives me that smaller value. If I was multiplying by 100, I should get a larger value. And moving the decimal to the right would give you that larger value.