3.1 Converting Among Ratio, Decimal & Percent

Morgan Chase and Marilyn Nielson

Learning Objectives (Sidebar)

When you’re finished with this chapter, you’ll be able to express a number as a ratio, decimal, or percent.

Applications

If four of of the 78 fish you examine from your screw trap display signs of whirling disease, what is the ratio of diseased fish to all fish captured? Can you report this as a decimal? As a percent?

Three juvenile rainbow trout deformed by whirling disease.

Three juvenile rainbow trout deformed by whirling disease.

 

The word percent means “per one hundred”. You can think of a percent as a fraction with a denominator of 100.

We learned how to set up a ratio in Section 2.5. We can take any ratio and convert it into a decimal or a percent. Similarly, we can take decimals and percents and express them as ratios.

Practice Exercises

  1. What percent of the squares are shaded blue?
  2. What percent of the squares are not shaded blue?

To write a percent as a fraction: drop the percent sign, write the number over 100, and simplify if possible. (Notice that if a percent is greater than 100%, the fraction will be greater than 1, and if a percent is less than 1%, the fraction will be less than [latex]\frac{1}{100}[/latex].)

To write a percent as a decimal: drop the percent sign and move the decimal point two places to the left (i.e. divide by 100). (Notice that if the percent is not a whole number, the decimal will extend beyond the hundredths place.)

To write a decimal as a percent: move the decimal point two places to the right (i.e. multiply by 100) and insert a percent sign.

To write a fraction as a percent, write the fraction as a decimal by dividing the numerator by the denominator, then move the decimal point two places to the right (i.e. multiply by 100) and insert a percent sign.

 

Ratio Decimal Percent
Ratio — Divide numerator by denominator Divide numerator by denominator. Then, multiply by 100 and add % sign.
Decimal Remove the decimal point and place the number as a numerator over a denominator of 1 with as many zeros as the places in the decimal. (e.g. 0.23 would get a denominator of 100; 0.345 would get a denominator of 1000). Reduce this fraction to lowest terms. — Multiply by 100 and add a % sign.
 Percent Remove the % sign. Put the number over 100. Reduce the fraction. Remove the % sign. Divide by 100. —

 

 

Examples

A) 0.34 to ratio     B) 0.756 to ratio     C) [latex]\frac{3}{5}[/latex] to decimal     D) latex]\frac{3}{5}[/latex] to percent     E) 0.86 to percent     F) 56% to ratio     G) 127% to ratio     H) 35% to decimal

View the answers.

Watch the solutions video.

Practice Exercises

a view o
Photo by NASA on Unsplash

Write each percent as a fraction, and simplify if possible.

  1. About [latex]71\%[/latex] of Earth’s surface is covered by water.[1]
  2. About [latex]1.3\%[/latex] of Earth’s land surface is permanent cropland.[2]
  3. About [latex]0.04\%[latex] of Earth’s atmosphere is carbon dioxide.[footnote]Source: https://en.wikipedia.org/wiki/Atmosphere_of_Earth#Composition[/footnote]
  4. The number of HVACR technician jobs in the U.S. in 2032 is predicted to be [latex]106\%[/latex] of the number of jobs in 2022.[3]

Practice Exercises

Write each percent from Exercises 3 through 6 as a decimal.

  1. [latex]71\%[/latex]
  2. [latex]1.3\%[/latex]
  3. [latex]0.04\%[/latex]
  4. [latex]106\%[/latex]

Practice Exercises

Write each decimal number as a percent.

  1. [latex]0.23[/latex]
  2. [latex]0.07[/latex]
  3. [latex]0.085[/latex]
  4. [latex]2.5[/latex]

Practice Exercises

15. [latex]7[/latex] out of [latex]25[/latex] students were tardy on Wednesday. Write [latex]\frac{7}{25}[/latex] as a percent.

16. A package of [latex]24[/latex] m&m’s contained [latex]3[/latex] orange m&m’s. Write [latex]\frac{3}{24}[/latex] as a percent.

 

 

Answers to Practice Exercises

 

Problem Set 3.1

Write each decimal as a percent.
  1. 0.26
  2. 0.385
  3. 26.58
Write each fraction as a percent.
  1. [latex]\frac{2}{3}[/latex]
  2. [latex]\frac{7}{8}[/latex]
  3. [latex]\frac{48}{72}[/latex]
  4. [latex]1\frac{1}{3}[/latex]
Write each percent as a decimal.
  1. 23%
  2. 5%
  3. 102%
Write each percent as a fraction in lowest terms or a mixed number.
  1. 10%
  2. 123%
  3. 0.4%

 

  1. Source: https://en.wikipedia.org/wiki/Earth#Surface ↵
  2. Source: https://en.wikipedia.org/wiki/Earth#Surface ↵
  3. Source: Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, Heating, Air Conditioning, and Refrigeration Mechanics and Installers, at https://www.bls.gov/ooh/installation-maintenance-and-repair/heating-air-conditioning-and-refrigeration-mechanics-and-installers.htm ↵

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