Calculating Percents

A percent is a ratio that compares a number to 100. The word percent (%) means “parts of 100” or “per 100 parts.” Another way to think of a percent is as a part of a whole expressed in hundredths. Thus, the number 0.41 (“41 hundredths”) can also be expressed as 41%, or “41 per 100 parts.”

You can calculate a percent by multiplying the ratio of the part to the whole by 100%.

Examples

The fraction $\genfrac{}{}{0.1ex}{}{7}{10}$ is equivalent to 70%.

The fraction $\genfrac{}{}{0.1ex}{}{5}{8}$ is equivalent to 62.5%.

The fraction $\genfrac{}{}{0.1ex}{}{15}{200}$ is equivalent to 7.5%.

You have probably seen data expressed in the form of a percent. For instance, nutrition labels on packaged foods include a column titled “% Daily Value.” In this column, the nutrients (such as fat, cholesterol, and fiber) contained in a single serving are compared to the recommended daily intake. You also encounter percents when you go shopping (items on sale might be labeled “20% off “) or when you receive test scores.

Example

A student answers 34 questions correctly on a 40-question exam. What is the student's score expressed as a percent?

Converting Between Percents and Decimals

To convert a percent to a decimal value, write the number without the percent sign and move the decimal point two places to the left. Add a zero before the decimal point.

Examples

You can convert a decimal value to a percent value by moving the decimal point two places to the right and adding the percent sign.

Examples

$0.46=46\%0.8215=82.15\%$

Converting between percents and decimals is often necessary when solving word problems involving composition or concentration.

Example

A nighttime cold medicine is 22% alcohol by volume. How many milliliters of alcohol are in a 250-mL bottle of this medicine?

Example

During a flu epidemic, 28% of the students at a school were absent. If 238 students were absent, what was the school's enrollment?