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### How to Divide Decimals by Decimals

```
Date: 03/07/98 at 19:16:53
From: Tiffany Wright
Subject: dividing decimals

I don't understand dividing decimals. Can you send me any information
so I can understand it more?

Thank you!

Tiffany Wright
```

```
Date: 03/08/98 at 11:33:30
From: Doctor Lim
Subject: Re: dividing decimals

Dear Tiffany,

Don't worry. Doing mathematics problems is just like eating a piece of
cake. Eating a piece of cake gets difficult when we try to eat a big
piece of cake all in one gulp. Let's break it into smaller pieces, and
we can eat it easier.

decimal:

0.2/0.5

It actually means
____
0.5 )0.2

We cannot have a divisor that is not a whole number, so we must change
0.5 into a whole number. To do this, we have to multiply by 10. This
is because 0.5 is in the tenths place. We have to do this for both the
divisor and the dividend in order to balance them.

0.2 x 10              2
-------------    =    -----
0.5 x 10              5

So, we have
____
5 )2.0

We need to show where the decimal point is in the dividend. The next
thing we need to do is to fix the decimal point of the answer. What
you do is just to move another decimal point straight up from the
position in the dividend.
___.___
5 ) 2.0

So, now you do normal division. Does 5 go into 2? No, so you can
either leave it blank, or put a zero there to remind yourself there's
nothing there (and it will ensure that you keep your decimal point in
the right place). Does 5 go into 20? Yes, so we put a 4 above the
zero. Our final answer is .4.

Now let's go through a more complicated problem:
______
0.14 )0.448

As above, we check out the divisor. The divisor is 0.14, which is 14
hundredths. So we have to multiply by 100.

0.448 x 100               44.8
-------------------   =  ----------
0.14 x 100                14

The first thing we do is take care of the decimal point of the divisor
(multiply by 100). So, we move the decimal of the dividend over two
places. Now we have
______
14 )44.8

Position the decimal point,
___.__
14 )44.8
xx.x
-------
xx.x

Once you have positioned the decimal point, divide the numbers as
usual. You should have no problem, because it is the same as division
of a big number, 448, divided by a smaller number, 14. The only
difference is that in your answer, you have to remember the position
of the decimal point.

Take things easy. Once you practise more often, you will find that it
gets easier and easier. Maths then will become a breeze.

-Doctor Lim, The Math Forum
Check out our web site http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Division
Elementary Fractions

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