by AuSmith » Wed Jul 22, 2009 1:58 am
Here's how I think of percent error. Imagine you have a princess seeking the perfect prince (meaning one that can read her mind). What does she do? She picks an integer between [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], then holds a contest to find the Prince who can correctly tell her the magic number. Of course, dozens of princes come to try their skill, some who guess well and some who apparently need to read up on their telepathy. Some would treat the contest much like a lottery. Some of the religious ones would spew off digits with absolute confidence until they were escorted out to the market place. Most guessed their own favorite numbers, for why would one pick anything else. While the princess waited, she thought of how she would deal with all these bozos. What if, after all, her perfect prince lost his social security card, refusing him his ever punctual lifestyle? Being versed in engineering, she uses her magic number as the standard by which all the attempts must be measured. So, for each attempt, she devises a percentage that she can multiply her magic number by to get the error for that attempt, which she calls "percent error."
[unparseable or potentially dangerous latex formula]
One uncommonly astute prince named Aero Smith (his real name was Gabriele Veneziano) knew some work the princess had done on the J function, and figured she would know that there is no number more magical than [unparseable or potentially dangerous latex formula]. Therefore, he boldly came before the princesses accountants declaring the magic number to be [unparseable or potentially dangerous latex formula]. Well, they got married and had two beautiful children. Nathaniel and... HOMFLY. Hahahahaha! Sooo inside.
Of course, Aero's percent error was [unparseable or potentially dangerous latex formula]. Then, the next closest was 168 (not a bad favorite number), with a percent error of [unparseable or potentially dangerous latex formula].
Wow. Umm, I got sidetracked. That's kind of what percent error is: [unparseable or potentially dangerous latex formula].
Percent difference naturally takes the first number to be the standard: [unparseable or potentially dangerous latex formula].
You then have to hammer through the unfortunate ambiguity and assume he's asking a valid question to arrive at the best interpretation. It's saying [unparseable or potentially dangerous latex formula] volts is the "exact" voltage... I guess because that's what it's supposed to be. Then, the beginning voltage [unparseable or potentially dangerous latex formula] and the end voltage [unparseable or potentially dangerous latex formula] should be approximations of [unparseable or potentially dangerous latex formula]. So, you find the percent error for [unparseable or potentially dangerous latex formula] volts, then for [unparseable or potentially dangerous latex formula] volts, and take the percent difference. It's important that [unparseable or potentially dangerous latex formula] appears first in the problem.