The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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

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

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 

   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 

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!
Associated Topics:
Elementary Fractions
Middle School Fractions

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.