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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

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