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## Staging content lifeboat

### Course: Staging content lifeboat > Unit 14

Lesson 52: Multiplying and dividing with powers of 10- Exponents and powers of 10 patterns
- Multiplying a decimal by a power of 10
- Dividing a decimal by a power of 10
- Dividing a decimal by a power of 10: pattern
- Multiply and divide by powers of 10
- Understanding moving the decimal
- Fractions as division by power of 10

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# Dividing a decimal by a power of 10

Sal talks about why moving the decimal point to the left when dividing by a power of 10 makes sense. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- If I had 72.3 times 23.5 how would I do that(12 votes)
- I am not going to judge how easy multiplying decimals is easy or not, but I will show you an O.P strategy of solving these kind of problems.

When solving these questions you should ignore the decimal points and multiply it like a whole number.

Then the number of decimals spaces from the original spaces will go to the answer.

That sounded pretty hard, but it's not.

Lets solve your problem 72.3 × 23.5.

SO lets ignore the decimals and multiply 723 × 235.

You should get 169905.

Now in the original equation there were two numbers and each of them had one place to the left so we will make it two places to the left because of the two numbers.

You should have gotten 1699.0(4 votes)

- How many times do you need to divide 4379.9 by ten to get 4.3799?(6 votes)
- You need to divide 4379,9 by 1000 to get 4,3799. That would mean you will need to divide it by 10 three times (10^3 = 1000).

An easy trick to remember, is to count how many spaces you have to move the point to the left. Here, you have to move it to the left 3 times (from 4379.9 to 4.3799), so you have to divide it by 10 three times.

Likewise, to go from 4.3799 to 4379.9, you have to move the point 3 spaces, but to the right this time. This means that you have to multiply 4.3799 by 10 three times to get 4379.9.(5 votes)

- Does that mean if you do 0.001 divided by 100 I would just move the decimal right 2 times?(4 votes)
- Move the decimal place
*left*two times. 0.001 divided by 100 = 0.00001. Place value goes up and down by powers of 10. Every time you multiply by 10, you go up a place value and every time you divide by 10, you go down a place value. When you divide 0.001 by 100, you’re basically dividing 0.001 by 10 twice, so you go down two place values.(3 votes)

- Please show a pattern that is easy to understand .. When multiplying a decimal by a power of ten(4 votes)
- Well, a pattern is:

0.001 * 10 = 0.01

0.001 * 100 = 0.1

0.001 * 1000 = 1

So, every time you multiply a number by ten you move the decimal place 1 place value to the right. And the same applies to numbers you usually don't see with decimal points, such as 1, 2, 3, etc.:

1*10 = ?(I know you probably already know this, but I'm providing an example)

Remember:

1.0 * 10 =

10.0(3 votes)

- why do you keep dividing the same number?(4 votes)
- Yea I don't know why he dose that(3 votes)

- why do we get a lower number(3 votes)
- Because when we divide, we change the whole number into groups of the whole number. For example, 4 divided by 2 means that only 2 groups of 2 will fit into 4, so 2 is the answer. Hope this helps! :D(5 votes)

- Do you always need to put a zero after the number after the decimal? For example, when your product for an answer is 3.20, do you have to keep that extra zero? Please reply A.S.A.P.(3 votes)
- No, 3.20 can just be written as 3.2. The zero on the end does not change the number.(4 votes)

- I got the viedo except for when you have to count the numbers behind the decimal I thought it was how many decimals(3 votes)
- What pattern describes how the decimal point moves when you multiply a decimal by any power of 10(3 votes)
- How do you divide whole numbers by fractions?(2 votes)
- turn the whole number into a fraction, like 15 divided by 1/8 would become 15/1 divided by 1/8. then you do what you usually do to divide a fraction by a fraction: flip the 1/8 to become 8/1, and multiply 15/1 x 8/1 (numerator times numerator and denominator times denominator) then you get 120/1. in other words, 120.(2 votes)

## Video transcript

We're asked to divide 99.061,
or 99 and 61/1000, by 100. And there's a few ways to do it. But what I want to
do in this video is focus on kind of a faster
way to think about it. And hopefully it'll
make sense to you. And that's also the focus of
it, that it makes sense to you. So 99, let's just think
about it a little bit. So if we-- so 99.061. So if we were to
divide this by 10, just to make the point clear, if
we were to divide this by 10, what would we get? Well, we would essentially
move the decimal place one spot to the left. And it should make sense because
we have a little over 99. If you took 99
divided by 10, you should have a little over 9. So essentially, you would
move the decimal place one to the left when
you divide by 10. So this would be
equal to 9.9061. If you were to divide it
by 100, which is actually the focus of this problem, so
if we divide 99.061 divided by 100, if we move the decimal
place once to the left, we're dividing by 10. To divide it by 100, we
have to divide by 10 again. So we move it over twice. So one, two times. And so now the decimal place
is out in front of that first leading 9, which also
should make sense. 99 is almost 100, or a
little bit less than 100. So if you divide it
by 100, we should be a little bit less than 1. And so if you move the
decimal place two places over to the left, because we're
really dividing by 10 twice, if you want to think
of it that way, we will get the decimal in
front of the 99-- 0.99061. We should put a zero out here. Just sometimes it
clarifies things. So then we get this
right over here. Now, one way to think
about it, although I do want you to always imagine that
when you move the decimal place over to the left, you really are
dividing by 10 when you move it to the left. When you move it to the right,
you're multiplying by 10. Sometimes people
say, hey, look, you could just count the
number of zeroes. And if you're dividing, so over
here, you were dividing by 100. 100 has two zeroes, and
we're dividing by it, so we could move our decimal
two spaces to the left. That's all right to do
that, especially it's kind of a fast way to do it. If this had 20 zeroes,
you would immediately say, OK, let's move the
decimal 20 places to the left. But I really want you to think
about why that's working, why that makes sense,
why it's giving you a number that seems to be the
right kind of size number, why it makes sense that if
you take something that's almost 100 and
divide by 100, you'll get something that's almost 1. And that part, frankly, is just
a really good reality check to make sure you're going
in the right direction with the decimal. Because if you tried
this 5, 10 years from now, maybe your
memory of the rule or whatever you want to
call it for doing it, you're like hey, wait,
do I move the decimal to the left or the right? It's really good to do that
reality check to say, OK, look, If I'm dividing by 100, I should
be getting a smaller value and moving the
decimal to the left gives me that smaller value. If I was multiplying by 100,
I should get a larger value. And moving the
decimal to the right would give you
that larger value.