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 [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.

Percent

A percent is a ratio whose denominator is [latex]100[/latex].

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.

The figure shows a hundred flat with 57 units shaded.
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.

example

According to the Public Policy Institute of California [latex]\left(2010\right)\text{, }\text{44%}[/latex] 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 [latex]44%[/latex]. [latex]44%[/latex]
Write the percent as a ratio. Remember that percent means per [latex]100[/latex]. [latex]\Large\frac{44}{100}[/latex]

 

Try it

 

example

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

 

try it