More Than 100 Percent

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

Please help to settle an ongoing argument with a friend: is it correct 
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.

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/