MathBench > Miscellaneous

Tricks with Division

Percent Change is not a direct comparison

It is important to note that percent change is not a direct comparison between two quantities.

antique gas pumpIf I directly compare the price of a gallon of gas in 2008 to a gallon in 1998, I get

$4.20 : $1.40 = 3:1 = 3

I could say “the ratio of gas prices is 3 to 1”

or “a gallon costs 3 times as much”

but the percent change is

($4.20 - $1.40) / $1.40 = 2 converted to percent -> 200%

I could say, “the price of gas has increased by 200%”

In common usage, like on the nightly news, these two different measures can sometimes get confused, but in your textbooks and labs, the distinction should be clear. In particular, any time you are asked to find the percent change, you should use the subtract-then-divide-by-the-baseline method.

Some practice:

What’s the percent change?

summer 1998: $1.40

October 2001: $1.90

Summer 2005: $2.40

Summer 2008: $4.20

Early 2009: $1.80

Notice that a 50 cent increase from 1998 to 2001 is a 36% change, while the same 50 cent increase from 2001 to 2005 is only a 26% increase. Why?

And remember that it is certainly possible to have a percentage change that is greater than 100%: for example, the price change from