Converting Fractions to Percents

Date: 04/24/2001 at 08:49:15
From: Kathy Donelli
Subject: Converting repeating fractions to percents

I am having problems trying to explain to my students how to show 
a fraction such as 4/9, 10/9, or 11/12 as a percentage. I know that 
you can divide to find a decimal or mixed decimal for each fraction, 
and then write the decimal as a percentage, but is there any rule to 
use as a guide as to how to show the answer? 

I also know that 1/3 = 33 1/3 %, but what do I do with the above kinds 
of fractions?

Thanks.

Date: 04/24/2001 at 12:34:21
From: Doctor Peterson
Subject: Re: Converting repeating fractions to percents

Hi, Kathy.

In converting a fraction to a percentage, there are two steps: convert 
to a decimal, and multiply by 100%. You are doing it in that order, 
but that is not necessary.

Instead, FIRST multiply by 100%, and THEN convert to a decimal or a 
mixed number.

For example,

    4/9 = 4/9 * 100% = 400/9 % = 44 4/9 %

I just multiplied by 100% and then divided; seeing that I was going to 
get a repeating decimal, I chose to write it as a mixed fraction 
instead. I could have written it as a repeating decimal:
       _
    44.4%

Of course, in many situations I would want to round off the decimal. 
Any of these answers would be acceptable, depending on the 
circumstances.

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