Dividing Two Decimals

Date: 8/30/95 at 16:23:1
From: Anonymous
Subject: Decimal Division

Dear Dr. Math,
          
I do not understand division when you are dividing a 
decimal into another decimal number. Please help!

From a 6th grade student in Mt. Vernon, New York

Date: 9/3/95 at 18:3:5
From: Doctor Heather
Subject: Re: Decimal Division

Hi.  I guess the best way I can help you is to give you 
a few examples, and try to explain exactly what I'm doing along 
the way.  

Let's start with dividing a one-place decimal into another 
one-place decimal:

.2/.5
   ___
.5 ).2

The first thing we need to do is take care of the decimal in the 
divisor position (.5).  This number must always be "changed" to a 
non-decimal. What I mean by "changed" is that we basically multiply 
both the divisor and the dividend by 10. [Check this out for yourself 
and see if you think this is okay. For example, is 100/20 the same 
as 1000/200?] The way I think of it is that you're moving the decimal 
of the dividend (.2) as many places to the right as there are decimal 
places in the divisor. In this case, the divisor only has one decimal 
place.

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. 
Just 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.
    _____
.14 ).448

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

Position the decimal point,
   ___.__
14 )44.8

and divide as usual. Try it out and see if you get 3.2  

If you have trouble, write back and try to explain some more, 
like a specific problem you're having trouble with. 

Good luck!

- Doctor Heather,  The Geometry Forum