Percents are used in many different applications. They are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by [latex]12\%[/latex] from last year, or that the number of jobless claims has increase by [latex]5\%[/latex] this quarter over last quarter.

Fig. 1: Unemployment rate as percent by year between 2004 and 2014.

We regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.

How many cents are in one dollar? There are [latex]100[/latex] cents in a dollar. How many years are in a century? There are [latex]100[/latex] 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 [latex]100[/latex]. We use the percent symbol [latex]\text{%,}[/latex] to show percent.

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

Among every [latex]100[/latex] community college students, [latex]57[/latex] are female.

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

Note that sometimes we need to insert a decimal point if a percent is stated as a whole number, and sometimes we need to insert leading zeros in order to move the decimal point two places to the left.

Often when a percent is converted to a ratio, a fraction is obtained which can be simplified. For example, [latex]25 \% = \frac{25}{100} = \frac{25 \cdot 1}{25 \cdot 4} = \frac{1}{4}[/latex]. Similarly, [latex]40 \% = \frac{40}{100} = \frac{20 \cdot 2}{20 \cdot 5} = \frac{2}{5}[/latex]