# Percents

### Percents

#### Percents

A percent employs a percent sign (%) followed by a number. It looks like this: 23%. A percent represents a fraction in which the number to the left of the % sign is the numerator and 100 is the denominator. "Percent" means "parts per hundred," or "out of 100." 23% is equivalent to 23 hundredths, or 23/100, or 0.23.

100% is equal to 100 out of 100, or 1. Percents greater than 100% are fractions (or decimals) greater than 1, while percents less than 100% are fractions (or decimals) less than 1.

#### Expressing Percents as Decimals

To convert a percent into a decimal, move the decimal point 2 places to the left and drop the percent sign. 36% becomes 0.36, and 145% becomes 1.45. If the number in front of the percent has fewer than two places in front of the decimal, add zeros to the left of the number, and then move the decimal place. For example, 5% = 05% = 0.05 and 1.78% = 01.78% = 0.0178 .

#### Expressing Decimals as Percents

To convert a decimal into a percent, move the decimal point two places to the right and add the % sign. If there are fewer than two places to the right of the decimal, add zeros at the end of the number after the decimal point. For example, 0.986 = 98.6% and 1.8 = 1.80 = 180% .

#### Expressing Percents as Fractions

As stated earlier, a percent is a fraction in which the number preceding the % sign is the numerator and 100 is the denominator. Therefore, the first step in writing a percent as a fraction in lowest terms is writing it as a fraction with denominator 100. For example, we write 82% as 82/100 and 50% as 50/100.

The next step is to reduce the fraction--see Fractions. 82/100 reduces to 41/50 and 50/100 reduces to 1/2. Thus, 82% = 41/50 and 50% = 1/2 .

If the number to the left of the % sign is not a whole number, first change the percent to a decimal, and then change the decimal to a fraction. For example, 67.4% = 0.674 = 674/1000 = 337/500 .

#### Expressing Fractions as Percents

The easiest way to change a fraction into a percent is first to change the fraction into a decimal by dividing the numerator by the denominator, and then change this decimal into a percent by moving the decimal point 2 places to the right, as above. For instance, 7/8 = 0.875 = 87.5% .

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