Multiplying and dividing decimals by 10

- [Instructor] We've already learned that when we multiply by 10, let's say we took the number 53 and we were to multiply it by 10, it has the effect of shifting all the digits once place to the left. So, this should be a review for you. But this was going to be 530. And we could see that what used to be in the tens place has been shifted to the left, to the hundreds place. And what used to be in the ones place has been shifted to the left to the tens place now. And we saw, if you divide by 10, you have the opposite effect. And so, let's say if I had 120, I could say, let's divide by 10, I could also say this is the same thing as 120 times 1/10. What is going to happen there? Well, in this situation, all the digits are going to shift one place to the right. So, what used to be in the tens place will now be in the ones place; what used to be in the hundreds place will now be in the tens place. So, this is just going to be equal to 12. So, that was all review. But now were going to extend this a little bit by thinking about things that have place values representing less than a one, I guess you could say, or we're gonna deal with decimals. So, just to get ourselves warmed up, let's see if we could figure out what 3.015 times 10 is. Pause this video, and see if you can figure that out. Well, the exact same thing is going to happen. All of our digits are going to shift one place to the left. So, right now, we have a three in the ones place, we have a zero in the tenths place, we have a one in the hundredths place, and we have a five in the thousandths, thousandths place. But now, they're all going to shift one place to the left. So, the three is now going to into the tens place, it's going to shift one place to the left. So, we're going to have, in the tens place, we are now going to have our three. And now, this zero, which was in the tenths place, is now going to shift into the ones place. So, the zero is going to go right over, the zero's going to go right over there. That is now in the ones place. And them we'll put our decimal. And now, what's going to go into the tenths place and the hundredths place? And actually, I'll rewrite the thousandths place as well. This one is going to shift one place to the left, into the tenths place, so into the tenths place. And then the five that was in the thousandths place is now going to shift one place to the left, into the hundredths place, so into the hundredths place, just like that. Now, we could put a trailing zero over here, but that's not going to change the value of this number, so I'll just leave it like that. And so, there you have it. We see that every digit has shifted one place to the left. So, this is equal to 30.15. I'll just put that zero there for kicks. And so, we could think about the other way around. What if I were to take 67.5, and if I were to divide it by 10, or another way of thinking about it is if I were to multiply this by 1/10. Pause the video, and see if you can figure out what that's going to be. Well, now, every digit is going to shift one place to the right. So, the six is going to be in the ones place, the seven is going to go into the tenths place, and then the five is going to go into the hundredths place. So, let's write that out. So, I have six is going to go into the ones place, and then we're gonna have our decimal point, our seven is going to go into the tenths place, and then our five is going to go into the hundredths place. So, there you have it, we get 6.75.