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Percents for Firefighter Exam Study Guide

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Updated on Jul 5, 2011

What Is a Percent?

A percent is a special kind of fraction or part of something. The bottom number (the denominator) in such a fraction is always 100. For example, 17% is the same as . Literally, the word percent means per 100 parts. The root cent means 100: A century is 100 years, there are 100 cents in a dollar, etc. Thus, 17% means 17 parts out of 100. Because fractions can also be expressed as decimals, 17% is also equivalent to .17, which is 17 hundredths.

You come into contact with percents every day. Sales tax, interest, and discounts are just a few common examples.

If you are shaky on fractions, you may want to review the fraction section before reading further.

Changing a Decimal to a Percent and Vice Versa

To change a decimal to a percent, move the decimal point two places to the right and tack on a percent sign (%) at the end. If the decimal point moves to the very right of the number, you don't have to write the decimal point. If there aren't enough places to move the decimal point, add zeros on the right before moving the decimal point.

To change a percent to a decimal, drop off the percent sign and move the decimal point two places to the left. If there aren't enough places to move the decimal point, add zeros on the left before moving the decimal point.

Try changing the following decimals to percent. The answers can be found at the end of this section on page 174.

1. .45
2. .008

Now change these percents to decimals:

1. 12%
2. 250%

Changing a Fraction to a Percent and Vice Versa

To change a fraction to a percent, there are two techniques. Each is illustrated by changing the fraction to a percent:

 Technique 1: Multiply the fraction by 100%. Multiply by 100%: Technique 2: Divide the fraction's bottom number into the top number; then move the decimal point two places to the right and tack on a percent sign (%). Divide 4 into 1 and move the decimal point 2 places to the right:

To change a percent to a fraction, remove the percent sign and write the number over 100. Then reduce if possible.

Example: Change 4% to a fraction.
1. Remove the % and write the fraction 4 over 100:
2. Reduce:

Here's a more complicated example: Change % to a fraction.

1. Remove the % and write the fraction over 100:
2. Since a fraction means "top number divided by bottom number," rewrite the fraction as a division problem:   ÷ 100
3. Change the mixed number () to an improper fraction ():       ÷
4. Flip the second fraction () and multiply:

Try changing these fractions to percents:

Now, change these percents to fractions:

1. 95%
2. 125%

Sometimes it is more convenient to work with a percent as a fraction or a decimal. Rather than have to calculate the equivalent fraction or decimal, consider memorizing the equivalence table on page 171. Not only will this increase your efficiency on the math test, but it will also be practical for real-life situations.