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### Percent Greater Than vs. Increased

```Date: 11/22/2002 at 15:20:11
From: Melissa Holmes
Subject: Percents

What is the difference between the following statements:

My profits are 200% bigger than they were last year.

and

My profits from last year have increased 200%.

This is one of the questions we have to answer in my Middle school
methods course and I have looked everywhere for the answer.  I hope
you can help.

Thank you.
```

```
Date: 11/23/2002 at 21:05:23
From: Doctor Peterson
Subject: Re: Percents

Hi, Melissa.

As far as I can see, they mean the same thing; in fact, both are
similarly ambiguous.

Taken literally, "200% bigger" (or, more formally, larger or greater)
and "increased 200%" (or, more completely, increased _by_ 200%) both
mean that the increase from one year to the next is 200% of the first
year's value, so that the second year's profit is 3 times the first.
But both statements are more likely to have been made with the
intention of saying that this year's profit is twice last years.
English is not very clear in cases like this.

Here is a related discussion in our archive, which deals mostly
with "two times greater" but mentions your case:

Larger Than and As Large As
http://mathforum.org/library/drmath/view/52338.html

Since writing that, I found a good reference on "two times greater,"
although it doesn't mention your "200% greater." It is in Merriam
Webster's _Dictionary of English Usage_, which under "times" writes

The argument in this case is that _times more_ (or _times larger_,
_times stronger_, _times brighter_, etc.) is ambiguous, so that
"He has five times more money than you" can be misunderstood as
meaning "He has six times as much money as you." It is, in fact,
possible to misunderstand _times more_ in this way, but it takes
a good deal of effort. If you have \$100, five times that is \$500,
which means that "five times more than \$100" can mean (the
commentators claim) "\$500 more than \$100," which equals "\$600,"
which equals "six times as much as \$100." The commentators regard
this as a serious ambiguity, and they advise you to avoid it by
always saying "times as much" instead of "times more." Here again,
it seems that they are paying homage to mathematics at the expense
of language. The fact is that "five times more" and "five times as
much" are idiomatic phrases which have - and are understood to
have - exactly the same meaning. The "ambiguity" of _times more_
is imaginary: in the world of actual speech and writing, the
meaning of _times more_ is clear and unequivocal. It is an idiom
that has existed in our language for more than four centuries,
and there is no real reason to avoid its use.

I think the same applies to "X percent bigger" and "increased [by]
X%." There is just enough ambiguity in a technical context that I
would want to ask what was intended before assuming anything, but
there is no reason to say that they definitely mean different things,
or mean something different than "X percent of" or "increased to X
percent." I myself would avoid saying these things, just because
there are enough people who have heard that they are ambiguous, and
would therefore take them the wrong way (whichever that is!).

If you have any further questions, feel free to write back. I'd be
interested to hear what the "correct" answer to this question is
supposed to be.

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

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