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### Dividing Decimals by Whole Numbers

```Date: 10/19/2002 at 16:14:39
From: Troubled
Subject: Dividing Decimals by whole numbers

Dividing decimals has been the hardest concept for me to learn.

- Troubled
```

```
Date: 10/19/2002 at 16:28:28
From: Doctor Ian
Subject: Re: Dividing Decimals by whole numbers

Hi,

Can you divide whole numbers by other whole numbers? For example, can
you do this?

219
_____
15 ) 3295
30
--
29
15
--
145
135
---
10

If so, then you can do the same thing with a decimal point:

2.1 9
________
15 ) 3 2.9 5
3 0
---
2 9
1 5
---
1 4 5
1 3 5
-----
1 0

You just leave the decimal point where it is. Now, what about that
remainder? Well, note that adding zeros to a decimal number after the
decimal point doesn't change the value of the number, e.g.,

32.95 = 32.950 = 32.9500 = ... = 32.950000000 = ...

So when you run out of other digits to bring down, you start bringing
down zeros instead:

2.1 9 6 6 6
______________
15 ) 3 2.9 5 0 0 0
3 0
---
2 9
1 5
---
1 4 5
1 3 5
-----
1 0 0
9 0
-----
1 0 0
9 0
-----
1 0

Now, when you do this, one of two things will eventually happen. The
first is that you'll end up with no remainder, in which case, you're
done.

The second thing that can happen is illustrated above: you fall into
a pattern where the same thing keeps happening over and over. In this
case, you're also done, and what you have is a repeating decimal. You
can indicate the repeating part by putting a bar over the pattern that
repeats. So in this case, we would get

2.1 9 6 6 6
______________           _
15 ) 3 2.9 5 0 0 0   =   2.196

So, to recap, dividing a decimal by a whole number works just like
dividing a whole number by a whole number, except there is a decimal
point (which you just leave where it is), and you keep adding zeros
at the end until you get no remainder, or until you get into a
repeating pattern.

I hope this helps. Write back if you'd like to talk more about this,
or anything else.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Division
Elementary Fractions
Middle School Division
Middle School Fractions

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