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More Than 100 Percent

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Date: 07/27/99 at 13:18:17
From: Michael
Subject: More than 100%?

to use a value of more than 100%? I say that there's no such thing
as anything larger than 100%; my friend says that it is okay to say
200% or 300% and so on.

Thank you.
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Date: 07/27/99 at 17:39:41
From: Doctor Rick
Subject: Re: More than 100%?

Hi, Michael.

There is nothing intrinsically wrong with using percentages greater
than 100%. Whether this makes sense depends entirely on the context.

A percentage is simply another way of writing a fraction with a
denominator of 100. For example, 6% = 6/100. Just as you can have an
improper fraction (a fraction whose numerator is greater than the
denominator), such as 4/3, so you can have what we might call an
"improper percentage" like 120% or 300%.

There are situations in which a percentage greater than 100% makes no
sense. For instance, "The Math Doctors answered 146% of the questions
received last month." This makes no sense because if we received 5061
questions, we couldn't possibly answer more than all of them. It's
just as nonsensical as saying "I ate 4/3 of the cake."

On the other hand, sometimes percentages are used like this: "The
number of questions received was up 15.7%, from 5450 in February to
6305 in March." In other words, the increase from February to March
was 6305-5450 = 855, and 855 is 15.7% of 5450. (These facts are true,
by the way.)

Now, what if the number of questions received went up to 14000 in
April? (It didn't.) This would be an increase of 122% from March to
April. There is nothing wrong with this - no law says that the number
of questions can't do more than double from one month to the next.

So the answer is, there is such a thing as a percentage larger than
100%, but not everything can have a percentage larger than 100%.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Middle School Fractions

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