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# Dividing decimals with hundredths

Decimal divisors in the hundredths place can be a little confusing. In this video we'll show you how to move the decimal and make it a whole number. Pretty nifty! Watch. Created by Sal Khan.

Video transcript

Let's see if we can divide
30.24 divided by 0.42. And try pausing the video
and solving it on your own before I work through it. So there is a couple of
ways you can think about it. We could just write it
as 30.24 divided by 0.42. But what do you do now? Well the important
realization is, is when you're doing a
division problem like this, you will get the
same answer as long as you multiply or divide both
numbers by the same thing. And to understand that,
rewrite this division as 30.42 over 0.42. We could write it
really as a fraction. And we know that when we
have a fraction like this we're not changing the
value of the fraction if we multiple the numerator
and the denominator by the same quantity. And so what could we
multiply this denominator by to make it a whole number? Well we can multiply it
by 10 and then another 10. So we can multiply it by a 100. So lets do that. If we multiply the
denominator by 100 in order to not change the
value of this, we also need to multiply the
numerator by 100. We are essentially
multiplying by 100 over 100, which is just 1. So we're not changing the
value of this fraction. Or, you could view this,
this division problem. So this is going to
be 30.42 times 100. Move the decimal two places
to the right, gets you 3,042. The decimal is now there
if you care about it. And, 0.42 times 100. Once again move the decimal
one, two places to the right, it is now 42. So this is going to be the
exact same thing as 3,042 divided by 42. So once again we can move the
decimal here, two to the right. And if we move that
two to the right, then we can move this
two to the right. Or we need to move
this two to the right. And so this is where,
now the decimal place is. You could view this as 3,024. Let me clear that
3024 divided by 42. Let me clear that. And we know how to tackle
that already, but lets do it step by step. How many times
does 42 go into 3? Well it does not go at all,
so we can move on to 30. How many times
does 42 go into 30? Well it does not go into 30
so we can move on to 302. How many times does
42 go into 302? And like always this is a bit
of an art when your dividing by a two-digit or a multi-digit
number, I should say. So lets think about
it a little bit. So this is roughly 40. This is roughly 300. So how many times
does 40 go into 300? Well how many times
does 4 go into 30? Well, it looks like
it's about seven times, so I'm going to try out
a 7, see if it works out. 7 times 2 is 14. 7 times 4 is 28. Plus 1 is 29. And now I can subtract. Do a little bit of
re-grouping here. So lets see, if I regroup--
I take a 100 from the 300. That becomes a 200. Then our zero tens,
now I have 10 tens, but I'm going to need
one of those 10 tens, so that's going to be 9 tens. And I'm going to
give it over here. So this is going to be a 12. 12 minus 4 is 8. 9 minus 9 is 0. 2 minus 2 is 0. So what I got left
over is less than 42, so I know that 7 is
the right number. I want to go as many
times as possible into 302 without going over. So now lets bring
down the next digit. Lets bring down
this 4 over here. How many times
does 42 go into 84? Well that jumps out at
you, or hopefully it jumps-- It goes two times. 2 times 2 is 4. 2 times 4 is 8. You subtract, and we
have no remainder. So 3,042 divided by
42 is the same thing as 30.42 divided by 0.42. And it's going to
be equal to 72. Actually, I didn't
have to copy and paste that, I'll just write this. This is equal to 72. Just like that.