Suppose you're taking the written test for your driver's license and you get \begin{align*} \frac{4}{5}\end{align*}

### Percent Problems

A **percent** is a ratio whose denominator is 100. Before we can use percents to solve problems, let's review how to convert percents to decimals and fractions and vice versa.

To convert a decimal to a percent, multiply the decimal by 100.

#### Example A

Convert 0.3786 to a percent.

\begin{align*}0.3786 \times 100=37.86\%\end{align*}

To convert a percentage to a decimal, divide the percentage by 100.

#### Example B

Convert 98.6% into a decimal.

\begin{align*}98.6 \div 100 = 0.986\end{align*}

When converting fractions to percents, we can substitute \begin{align*}\frac{x}{100}\end{align*}

#### Example C

*Express* \begin{align*}\frac{3}{5}\end{align*}*as a percent.*

We start by representing the unknown as \begin{align*}x\%\end{align*}

\begin{align*}\left (\frac{3}{5} \right) & = \frac{x}{100} && \text{Cross multiply}. \\
5x & = 100 \cdot 3 \\
5x & = 300 \\
x & = \frac{300}{5} = 60 && \text{Divide both sides by}\ 5\ \text{to solve for}\ x. \\
\left (\frac{3}{5} \right) & = 60\%\end{align*}

### Video Review

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### Guided Practice

*Express 75% as a reduced fraction.*

**Solution:**

75% means \begin{align*}\frac{75}{100}.\end{align*}

\begin{align*}\frac{75}{100}=\frac{3\times 25}{4\times 25}=\frac{3}{4}.\end{align*}

### Explore More

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Percent Problems (14:15)

Express the following decimals as percents.

- 0.011
- 0.001
- 0.91
- 1.75
- 20

Express the following fractions as a percent (round to two decimal places when necessary).

- \begin{align*}\frac{1}{6}\end{align*}
16 - \begin{align*}\frac{5}{24}\end{align*}
524 - \begin{align*}\frac{6}{7}\end{align*}
67 - \begin{align*}\frac{11}{7}\end{align*}
117 - \begin{align*}\frac{13}{97}\end{align*}
1397

Express the following percentages as reduced fractions.

- 11%
- 65%
- 16%
- 12.5%
- 87.5%

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 3.9.