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 %, to show percent.

Percent

A percent is a ratio whose denominator is 100.

According to data from the American Association of Community Colleges (2015), about 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 57100.

Among every 100 community college students, 57 are female.

The figure shows a hundred flat with 57 units shaded.
Similarly, 25% means a ratio of 25100,3% means a ratio of 3100 and 100% means a ratio of 100100. In words, “one hundred percent” means the total 100% is 100100, and since 100100=1, we see that 100% means 1 whole.

example

According to the Public Policy Institute of California (2010)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. 44100

 

Try it

 

example

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

 

try it