Percent Difference Between Two Number

[wahaj]

I am a bit embarrassed to ask this question as I can do multivariable calculus but I can't seem to figure out this simple percentage question. My professor calculated percent difference using two different formulas and I am can't figure out what the difference is between the two. Here are the formulas
$$error = \frac{larger value - smaller value}{larger value} X 100$$
and
$$error = \frac{larger value - smaller value}{smaller value} X 100$$
can anyone explain where the second formula would be used because so far I've only used the first formula.

Mod note: The % signs were fouling up the LaTeX, so I removed them. Office_Shredder must have removed them in what he copied.

 

[Office_Shredder]

I am a bit embarrassed to ask this question as I can do multivariable calculus but I can't seem to figure out this simple percentage question. My professor calculated percent difference using two different formulas and I am can't figure out what the difference is between the two. Here are the formulas
$$error = \frac{larger value - smaller value}{larger value} X 100$$
and
$$error = \frac{larger value - smaller value}{smaller value} X 100$$
can anyone explain where the second formula would be used because so far I've only used the first formula.

It depends on whether you're interested in the percent change of the larger or smaller number. For example if the government deficit is 500 billion dollars, then grows to 600 billion dollars, it grew by 100/500*100 = 20 percent. If it was 600 billion dollars, then shrunk to 500 billion dollars, then it shrunk by 100/600*100 = 16.6 percent.

 

[wahaj]

[STRIKE]I get what you are trying to say. One more question, if I wanted to find the greatest percent difference between the two numbers I would use the second formula?
[/STRIKE]
[edit] never mind I figured it out.