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Study Guide

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A **percent** is an abbreviation for a fraction where the denominator is 100. That fancy "%" sign means "over 100." So that 64% you got on your history pop quiz last week? Yeah, that wasn't actually out of 70, sorry to say. You might want to hold off on the bragging.

Check it out:

^{3}/_{100} = 3%^{42}/_{100} = 42%^{200}/_{100} = 200%

Notice that each of these fractions has a denominator of 100, so we can also write them as decimals:

3% = ^{3}/_{100} = 0.03

42% = ^{42}/_{100} = 0.42

200% = ^{200}/_{100} = 2

To get from a decimal to a percent, we move the decimal point two places to the right (because there are two zeros in 100) and add a percent sign. Take a gander:

0.25 = 25%

0.1 = 10%

0.366 = 36.6%

When doing arithmetic with percents, it's usually easiest to turn them back into fractions or decimals first. Percents aren't the easiest things to work with, but they sure are nice for labeling milk.

To get from a percent to a decimal, move the decimal point two places to the left and erase the percent sign. Or, if your eraser doesn't work on your computer monitor, hit the "delete" key.

Remember that when it comes to fractions, "of" means "multiply." Since percents are abbreviations for fractions, this is also true for percents: "55% of 400" means "55% × 400," or "0.55 × 400." It's like we have our own secret language. Hey, let's also have "sundial" stand for "banana peanut butter sandwich." Man, we could go for a sundial right now. *Wink*.

### Portion of the Whole

A percent is secretly just a fraction where the denominator is 100. However, we can also think of a percent as telling how much a part is of the whole. For example, if 75% of all charts used to demonstrate percents are in the form of pie charts, you could demonstrate that by filling in

^{3}/_{4}of a pie chart. Ooh, we hope that doesn't skew our data.To figure out what percent

*a*is of*b*, write the fraction^{a}/_{b}and convert it into a decimal. Then change the decimal to a percent.### Sample Problem

What percent is 6 of 24?

^{6}/_{24}=^{1}/_{4}= 0.25 = 25%So if you watch

*Mad Men*for 6 hours, that's 25% of your day you've spent watching TV.*Oof*.The question could also be phrased, "What percent of 24 is 6?" The number after the word "of" is the whole, and the other number is the part. Don't always assume the bigger number is the whole, however. You might also be asked, "what percent of 6 is 24?" The answer to that one would be 400%. Which is

*definitely*too much television.

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