Writing Percents as Ratios

Learning Outcomes

• Use the definition of percent
• Write a percent as a ratio
• Given a ratio, write as a percent and a fraction

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 $\left(2015\right)$, about $\text{57%}$ of community college students are female. This means $57$ out of every $100$ community college students are female, as the image below shows. Out of the $100$ squares on the grid, $57$ are shaded, which we write as the ratio $\Large\frac{57}{100}$.

Among every $100$ community college students, $57$ are female.

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

example

According to the Public Policy Institute of California $\left(2010\right)\text{, }\text{44%}$ 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 $100$. $\Large\frac{44}{100}$

example

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.