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/