33 1/3 Percent as a Fraction

Date: 08/03/2003 at 12:50:41
From: Nerd
Subject: Percents

I need help turning percents like 33 1/3%, 2.5%, and other percents 
like that into fractions. Can you help me?

Date: 08/03/2003 at 15:47:31
From: Doctor Ian
Subject: Re: Percents

Hi Nerd,

The thing to remember about a percentage is that it's just a fraction
with a denominator of 100.  That's all it is.  

So 22% is exactly the same as 22/100.  This means that 33% is the same
as 33/100, and 33 1/3% is the same as 

  33 1/3
  ------
    100

Now, this is a pretty ugly fraction. It would be nicer-looking if we
multiplied the numerator and denominator by 3, which changes the
appearance without changing the value:

  33 1/3   3   100
  ------ * - = ---
    100    3   300

And this can be simplified to 1/3. 

Now, what about 2.5%?  This is the same as
 
   2.5
   ---
   100

This would be nicer looking if we got rid of the decimal places, which
we can do by multiplying the numerator and denominator by powers of 
10:

   2.5   10    25
   --- * -- = ----
   100   10   1000

This, too, can be simplified.  I'll leave that to you. 

But this is the basic idea: Put the percentage in the numerator, make 
the denominator 100, and do what you have to do to get an integer in 
the numerator. Then simplify. 

Does this make sense? 

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

Date: 08/03/2003 at 18:25:42
From: Nerd
Subject: Thank you (Percents)

Thank you so much for the help. You have helped me understand this 
concept really well!