Place value when multiplying and dividing by 10

- [Voiceover] What is 7 100s times 10? Well, let's focus first on this times 10 part of our expression. Because multiplying by 10 has some patterns in math that we can use to help us solve. One pattern we can think of when we multiply by 10 is if we take a whole number and multiply it by 10, we'll simply add a zero to the end of our whole number. So, for example, if we have a whole number like nine, and we multiply by 10, our solution will be a nine with one zero at the end. Or 90. Because nine times 10 is the same as nine 10s, and nine 10s is ninety. So let's use that pattern first to try to solve. Here we have seven 100s. So, seven times we have 100, or 700, and we're multiplying again times 10. Use this pattern over here. Our solution will add a zero at the end. So if we had 700, 10 times, we would have 700 with a zero on the end. Or 7,000. So seven 100s times ten, is equal to 7,000. But there's another pattern we could use, here. Another pattern to think about when we multiply by 10. And that is that when we multiply by 10, we move every digit one place value, one place value, left. Or one place value greater. So let's look at that one on a place value chart. Here we have a place value chart. To use that earlier example when we had nine ones, and we multiplied it by 10, our nine moved one place value to the left. It moved up to the 10s. Now, we had nine 10s. And we filled in a zero here, because there were no ones left; there were zero ones left. And so, we saw that nine times 10 was equal to 90. So again, it's the same as adding a zero at the end, but we're looking at it another way. We're looking at it in terms of place value and multiplying by 10 moved every digit one place value to the left. So, if we do that with this same question, seven 100s, seven 100s, if we move 100s one place value to the left, we'll end up with 1,000s. So, 700 times 10 is seven 1,000s. Or, as we saw earlier, 7,000. So either one of these is a correct answer. 700 times 10 is 7,000. And here's an example with division. Now we have dividing by 10. And as you might predict, dividing by 10 is the opposite of multiplying by 10, so our patterns are also the opposite. Instead of adding a zero to the end of a whole number, we would drop a zero at the end. We would drop a zero at the end. So, for an example, if we had 40, divided by 10, we would drop that zero and end up with four. If you divide 40 into groups of 10, you have four groups. Let's use that over here. 212 10s. So we have 212 10s. So 212, 10 times. That's how we got the zero, there. And we divide that by 10, we can use this first pattern we thought of and just drop the zero on the end. Let's drop that zero, and our answer will be 212. But we could also, we could use the place value pattern. We could think in terms of place value. And instead of moving one place value to the left, one place value larger, we're gonna move one place value smaller. Or to the right. One place value to the right. So what's one place value smaller than 212 10s? If we have 212 10s, divided by 10, we wanna move this 10s one place value to the right, or smaller, which is ones. So our solution would be 212 ones. Which is equal to what we already saw, simply 212. So 212 10s, divided by 10. We could write the number out and drop a zero, or we could think about place value and move one place value to the right. Either way, our answer is 212 ones.