Associated Topics || Dr. Math Home || Search Dr. Math

### Converting Ratios to Percentages

```Date: 08/03/2003 at 18:00:45
From: Dee
Subject: Converting ratios into percentages

How do I convert 1:200 to a percentage?
```

```
Date: 08/03/2003 at 23:01:12
From: Doctor Ian
Subject: Re: Converting ratios into percentages

Hi Dee,

Suppose the ratio of farmers to cows is 1 to 200. That means that for
every farmer, there are 200 cows. In any group of farmers and cows,
the fraction of farmers would be

farmers          1          1
-------------- = ------- = ---
farmers + cows   1 + 200   201

So how can we convert that to a percentage?  What we want to do is
solve this proportion:

1     ?
--- = ---
201   100

(It's important to understand that something like '12 percent' is just
another way to express a fraction like 12/100, which has a denominator
of 100. So

1% = 1/100

38% = 38/100

26.44512% = 26.44512 / 100

and so on.)

If we multiply both sides by 100, we get

100
--- = ?
201

If we divide 100 by 201 (using a calculator), we get 0.4975, which is
about 0.5, so the farmers make up 1/2 percent of the membership of the
group.

Does this make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions
Middle School Ratio and Proportion

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