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### Course: Arithmetic (all content) > Unit 1

Lesson 8: How 10 relates to place value- Multiplying whole numbers by 10
- Multiply whole numbers by 10
- Dividing whole numbers by 10
- Divide whole numbers by 10
- Multiply and divide by 10
- Understanding place value
- Comparing place values
- Place value when multiplying and dividing by 10
- Place value when multiplying and dividing by 10

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# Place value when multiplying and dividing by 10

Lindsay discusses how multiplying and dividing by 10 affects place value.

## Want to join the conversation?

- If you multiply 10 x 9 you add a zero

Why don't you get 90 when the problem is 9 x 0(19 votes)- What she meant when she said "if you multiply 10 x 9 you add a zero," what she meant was you add a zero to the answer you got. because 10 x 9 = 90. see? there is a zero at the end! :3(30 votes)

- when we multiply a number by 5 , the number has
*__*or*__*in the one place.(17 votes)- Like skip counting by 5 like 5 10 15 20 26 30 35 40 45 50 55 60 you can go to 100 65 70 75 80 85 90 95 100(8 votes)

- If you just divide a number by ten and it has zeros, take out a zero. Very easy(14 votes)
- right! just remember that the zeroes you take out have to be at the end, like 100, not 101(17 votes)

- and if you divide by ten you drop a zero or you can move one place value to the right(4 votes)
- if you multiply by ten you add a zero at the end of the original number(4 votes)
- Try watching the video again.(4 votes)
- so it is adding a 0 right(4 votes)
**hi**can i get an explantion because i didn't get it at all!(3 votes)- When you have a number like 100 and you divid it by 10 you take one of the zeros away. 10. Same for multiplying but you add a zero(2 votes)

- how can you multiply a decimal?(3 votes)
- Multiplication of decimals is same as integers for example 7.96*6.8 = 54.128 we kept decimal after 3 digits because in 7.96 there are 2 digits after decimal and in 6.8 there is one digit after decimal total 3 digits. so, after multiplying we have to keep decimal after 3 digits from left side.(2 votes)

- Did we not learn this before the last video? (Not including lessons)(3 votes)

## Video transcript

- [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.