Representing Rational Numbers

Date: 09/17/2002 at 19:38:34
From: Kellsey
Subject: Percents, fractions, decimals

What do fractions, decimals, and percents have in common?

Date: 09/18/2002 at 10:15:20
From: Doctor Ian
Subject: Re: Percents, fractions, decimals

Hi Kellsey,

They're all just different ways of representing rational numbers. 
 
For example, let's look at the decimal number 0.125.  What this 
_means_ is

  0.125 = 0 + 1/10 + 2/100 + 5/1000

That is, each decimal place corresponds to a different fraction, and 
the number itself is the sum of these fractions.  

Now, suppose we adjust this so that all the fractions have a 
denominator of 100:

  0.125 = 0 + 10/100 + 2/100 + 0.5/100

Now we can use the distributive property to add them together:

  0.125 = 0 + (10 + 2 + 0.5)/100

        = 12.5/100

A fraction whose denominator is 100 is given the special name of 
'percent' (which literally means 'for each hundred'). So 

  0.125 = 12.5%

But can we make this fraction simpler? In fact, we can:

  12.5/100 = 25/200

           = 1/8
So

  0.125 = 12.5% = 1/8

Now, all of these mean exactly the same thing, but they're different 
ways of writing it. Which form you use depends on what you're trying 
to do. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/