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/