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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!
```
Associated Topics:
Elementary Fractions
Middle School Fractions

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