Multiplying and dividing decimals by 10, 100, 1000

- [Instructor] In this video, we're going to get a little bit of practice multiplying and dividing decimals by 10, 100, and 1000. So let's just start with a little bit of a warmup. If I were to say, what is 2.05 times 10? Pause this video and see if you can figure that out. Well, in previous videos, we've already said that when you multiply by 10, you shift each of the digits one place to the left. And so this is going to be equal to, instead of two ones, we're now going to have two 10s, so two in the tens place. And then, instead of zero tenths, we're now going to have zero ones. And instead of five hundredths, we're now going to have five tenths, so this is equal to 20.5. Now what if we were to go the other way around? What if we were to say 2.05 divided by 10? Pause the video and see if you can figure that out. Well here, all of our digits are going to shift one place to the right because we're dividing by 10. You could also view that as multiplying by 1/10. And so our two ones are going to become two tenths, so this is going to be zero point, so we're gonna have two tenths now. Our zero tenths are going be zero hundredths, and then our five hundredths are going to be five thousandths, we've covered that in other videos, but now let's do this with, say, 100 or 1000. So if I were to ask you what is 57 divided by 1000? Pause this video and see if you can work that out. All right, now let's do this together. So when you divide by 1000, that's the same thing as dividing by 10 three times. Or it's the same thing as multiplying by 1/10 three times, or you could just say hey, that means I'm going to shift each of these digits three places to the right, and so let me create some places here. So that's 10s, ones, tenths, hundredths, thousandths, and so our five was in the 10s place, it's five 10s, so it was here, but we're going to shift three places to the right. One, two, three. So our five will go there. So what was five 10s is now five hundredths. And then our seven is similarly going to, it was in the ones place, but we're gonna shift three places to the right. One, two, three. And there you have it. What was just 57 is now 57 thousandths. And to make that very clear, I'll put a zero in the tenths place and a zero in the ones place, and that makes sense. So as another example, let's say someone walks up to you on the street and says I started with 1.032 and I multiplied it by something and I was able to get 103.2. What did they multiply by to get 103.2? Pause this video and try to work it out. Well to understand this, we just have to think well, how much did each digit get shifted by? So what was in the ones place got shifted not just to the 10s place, but it got shifted to the hundreds place. So it got shifted two places to the left. The zero, similarly, got shifted two places to the left. From the tenths to the 10s, and if you look at it, every digit got shifted two places to the left. And we must have multiplied by 10 twice, so you could say times 10 times 10, or you could just rewrite this as times 100. Let's just do one more example for kicks. Let's say that someone were to say what is 0.015 times 100? Pause this video and see if you can figure that out. All right, well, like we've done before, we're just going to shift every digit two places to the left. So the one, which is in the hundredths place, is going to end up in the ones place, and then the five, which is in the thousandths place, is going to end up in the tenths place. So this is going to be equal to 1.5, and we're done.