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### Course: Arithmetic > Unit 17

Lesson 2: Multiplying and dividing decimals by 10, 100, and 1,000# Multiplying and dividing decimals by 10, 100, 1000

Explore the concept of multiplying and dividing decimals by 10, 100, and 1000. Learn how each digit in a decimal number shifts places when multiplied or divided by these powers of 10, providing a visual and intuitive understanding of the process.

## Want to join the conversation?

- Why do you have to say tenths or ones. For example 3 tenths or 5 ones.(13 votes)
- Great question! Well, it is not 100 percent determined but I think mathematicians just decided to do it.(26 votes)

- Wait... I thought that when we multiply we move places to the right..?(12 votes)
- Yes, that is correct. I would like to add that when you divide, you move the decimal to the left. I hope this helped!(13 votes)

- Wait-I thought that when we multiply we move places to the right..?(6 votes)
- No Jaiden , when you multiply it goes one place to the left.(6 votes)

- how do i divide and multiply decimals(7 votes)
- When you divide a number like 10.4 by 10, since you're dividing it the numbers move one place value to the right, if you're dividing it by 100, then it moves two places to the right. For multiplying, you move the digits to the left(3 votes)

- For anyone confused, here's a neat guide for you.

When you multiply a number by 10:

- The decimal point shifts over to the**right**one time.

- The place value shifts over to the**left**one time.

For example, take the number 29. We know that there is an imaginary decimal point at the end of every whole number, so if we shift the decimal point one place to the right, it becomes 290.

Basically, we shifted the decimal point to the right, but our place values got shifted left. The number 9 which used to be in the ones place was moved to the tens place and a zero was put in the ones place instead. The number 2 which used to be in the tens place was moved to the left one time, which is the hundreds place.

The same rules apply to division but in reverse.

When you divide a number by 10:

- The decimal point shifts over to the**left**one time.

- The place value shifts over to the**right**one time.

Hope this helps and good luck to everyone!(6 votes) - im bad at math in general so like...ya(5 votes)
- how do you do this problem(1 vote)
- How do you do it verticaly(1 vote)
- in time stamp2:01I'm i right you need to shift the decimal place value to the left Because you need to shift the decimal place value to the right(1 vote)
- I honestly feel like moving the decimal might be easier than moving every single digit.(1 vote)

## Video transcript

- [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.