# 6.1 Understand percent

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By the end of this section, you will be able to:
• Use the definition of percent
• Convert percents to fractions and decimals
• Convert decimals and fractions to percents

Before you get started, take this readiness quiz.

1. Translate “the ratio of $33$ to $\text{5”}$ into an algebraic expression.
If you missed this problem, review Evaluate, Simplify and Translate Expressions .
2. Write $\frac{3}{5}$ as a decimal.
If you missed this problem, review Decimals and Fractions .
3. Write $0.62$ as a fraction.
If you missed this problem, review Decimals .

## Use the definition of percent

How many cents are in one dollar? There are $100$ cents in a dollar. How many years are in a century? There are $100$ years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A percent    is a ratio whose denominator is $100.$ We use the percent symbol $\text{%,}$ to show percent.

## Percent

A percent is a ratio whose denominator is $100.$

According to data from the American Association of Community Colleges $\left(2015\right)\text{,}$ about $\text{57%}$ of community college students are female. This means $57$ out of every $100$ community college students are female, as [link] shows. Out of the $100$ squares on the grid, $57$ are shaded, which we write as the ratio $\frac{57}{100}.$

Similarly, $\text{25%}$ means a ratio of $\frac{25}{100},\text{3%}$ means a ratio of $\frac{3}{100}$ and $\text{100%}$ means a ratio of $\frac{100}{100}.$ In words, "one hundred percent" means the total $\text{-100%-}$ is $\frac{100}{100},$ and since $\frac{100}{100}=1,$ we see that $\text{100%}$ means $1$ whole.

According to the Public Policy Institute of California $\left(2010\right)\text{,}\phantom{\rule{0.2em}{0ex}}\text{44%}$ of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.

## Solution

 The amount we want to convert is 44%. $44%$ Write the percent as a ratio. Remember that percent means per 100. $\frac{44}{100}$

Write the percent as a ratio.

According to a survey, $\text{89%}$ of college students have a smartphone.

$\frac{89}{100}$

Write the percent as a ratio.

A study found that $\text{72%}$ of U.S. teens send text messages regularly.

$\frac{72}{100}$

In $2007,$ according to a U.S. Department of Education report, $21$ out of every $100$ first-time freshmen college students at $\text{4-year}$ public institutions took at least one remedial course. Write this as a ratio and then as a percent.

## Solution

The amount we want to convert is $21$ out of every $100.$

 Write as a ratio. $\frac{21}{100}$ Convert the 21 per 100 to percent. $21%$

Write as a ratio and then as a percent: The American Association of Community Colleges reported that $62$ out of $100$ full-time community college students balance their studies with full-time or part time employment.

$\frac{62}{100},\text{62%}$

Write as a ratio and then as a percent: In response to a student survey, $41$ out of $100$ Santa Ana College students expressed a goal of earning an Associate's degree or transferring to a four-year college.

$\frac{41}{100},\text{41%}$

## Convert percents to fractions and decimals

Since percents are ratios, they can easily be expressed as fractions. Remember that percent    means per $100,$ so the denominator of the fraction is $100.$

## Convert a percent to a fraction.

1. Write the percent as a ratio with the denominator $100.$
2. Simplify the fraction if possible.

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