Date: Tue, 16 Mar 1999 08:38:07 -0600 (CST)
Subject: Percentages

Name: Beth

Question:
If I have two figures and want to know the difference between them, in Percentage, how do I proceed with a calculation?

Example: 67,800 - 56,000 = 11,800
What percentage does this difference represent?

It's been about 0 years since High School, so I don't remember how to do this.
Thank-you!

Hi Beth

You are asking a very important question. Whenever we talk about percent we have to ask "of what?".Consider this example.

A $100 item is increased in price by 10% and then the new price is decreased by 10%. Are you back to where you started? Let's try it. 10% means 0.10 so 10% of $100 is 0.1x100 = 10 and so the new price is $110 (10 + 10). Now we want to calculate the decrease in price.  But the decrease is 10% of $110 and so the decrease is 0.10x110 = 11 and so the new price is $99 (110 - 11). Surprise!
    Now to return to your problem. The answer depends on whether you want to determine the difference as a percent of 56 000 or as a percent of 67 800. If you want the difference as a percent of 56 000 then you write the fraction 11 800/56 000.  If you want the difference as a percent of 67 800 then you write the fraction  11 800/67 800. In the 1st case the decimal is 0.2107.... To change this to a percent we multiply by 100 and so the difference as a percent of 56 000 is about 21.1%. In the 2nd case the decimal is 0.1740... and so the difference as a percent of 67 800 is about 17.4%. I hope that this helps.

Jack

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