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Study Guides > Mathematics for the Liberal Arts Corequisite

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 100100 cents in a dollar. How many years are in a century? There are 100100 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 100100. We use the percent symbol \text{%,} to show percent.

Percent

A percent is a ratio whose denominator is 100100.
According to data from the American Association of Community Colleges (2015)\left(2015\right), about \text{57%} of community college students are female. This means 5757 out of every 100100 community college students are female, as the image below shows. Out of the 100100 squares on the grid, 5757 are shaded, which we write as the ratio 57100\Large\frac{57}{100}. Among every 100100 community college students, 5757 are female. The figure shows a hundred flat with 57 units shaded. Similarly, \text{25%} means a ratio of \Large\frac{25}{100}\normalsize ,\text{3%} means a ratio of 3100\Large\frac{3}{100} and \text{100%} means a ratio of 100100\Large\frac{100}{100}. In words, "one hundred percent" means the total \text{100%} is 100100\Large\frac{100}{100}, and since 100100=1\Large\frac{100}{100}\normalsize =1, we see that \text{100%} means 11 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 4444%. 4444%
Write the percent as a ratio. Remember that percent means per 100100. 44100\Large\frac{44}{100}
 

Try it

[ohm_question]146655[/ohm_question]
 

example

In 20072007, according to a U.S. Department of Education report, 2121 out of every 100100 first-time freshmen college students at 4-year\text{4-year} public institutions took at least one remedial course. Write this as a ratio and then as a percent.

Answer: Solution

The amount we want to convert is 2121 out of 100100 . 2121 out of 100100
Write as a ratio. 21100\Large\frac{21}{100}
Convert the 2121 per 100100 to percent. 2121%

 

try it

[ohm_question]146656[/ohm_question]

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