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Study Guides > Mathematics for the Liberal Arts Corequisite

Writing Decimals and Fractions as Percents

Learning Outcomes

  • Convert a decimal to a percent
  • Convert a fraction to a percent
To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is [latex]100[/latex], it is easy to change that fraction to a percent.

Convert a decimal to a percent.

  1. Write the decimal as a fraction.
  2. If the denominator of the fraction is not [latex]100[/latex], rewrite it as an equivalent fraction with denominator [latex]100[/latex].
  3. Write this ratio as a percent.
 

example

Convert each decimal to a percent: 1. [latex]0.05[/latex] 2.[latex]0.83[/latex] Solution
1.
[latex]0.05[/latex]
Write as a fraction. The denominator is [latex]100[/latex]. [latex]{\Large\frac{5}{100}}[/latex]
Write this ratio as a percent. [latex]5[/latex]%
2.
[latex]0.83[/latex]
The denominator is [latex]100[/latex]. [latex]{\Large\frac{83}{100}}[/latex]
Write this ratio as a percent. [latex]83[/latex]%
 
 

try it

[ohm_question]146666[/ohm_question]
To convert a mixed number to a percent, we first write it as an improper fraction.

example

Convert each decimal to a percent: 1. [latex]1.05[/latex] 2. [latex]0.075[/latex]

Answer: Solution

1.
[latex]0.05[/latex]
Write as a fraction. [latex]1{\Large\frac{5}{100}}[/latex]
Write as an improper fraction. The denominator is [latex]100[/latex]. [latex]{\Large\frac{105}{100}}[/latex]
Write this ratio as a percent. [latex]105[/latex]%
Notice that since [latex]1.05>1[/latex], the result is more than [latex]\text{100%.}[/latex]
2.
[latex]0.075[/latex]
Write as a fraction. The denominator is [latex]1,000[/latex]. [latex]{\Large\frac{75}{1,000}}[/latex]
Divide the numerator and denominator by [latex]10[/latex], so that the denominator is [latex]100[/latex]. [latex]{\Large\frac{7.5}{100}}[/latex]
Write this ratio as a percent. [latex]7.5[/latex]%

 

try it

[ohm_question]146667[/ohm_question] [ohm_question]146668[/ohm_question]
Let's summarize the results from the previous examples in the table below so we can look for a pattern.
Decimal Percent
[latex]0.05[/latex] [latex]\text{5%}[/latex]
[latex]0.83[/latex] [latex]\text{83%}[/latex]
[latex]1.05[/latex] [latex]\text{105%}[/latex]
[latex]0.075[/latex] [latex]\text{7.5%}[/latex]
Do you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign. The next table uses the decimal numbers in the table above and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the [latex]%[/latex] sign. The figure shows two columns and five rows. The first row is a header row and it labels each column In an earlier lesson, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.

Convert a fraction to a percent

  1. Convert the fraction to a decimal.
  2. Convert the decimal to a percent.
 

example

Convert each fraction or mixed number to a percent: 1.  [latex]{\Large\frac{3}{4}}[/latex] 2.  [latex]{\Large\frac{11}{8}}[/latex] 3.  [latex]2{\Large\frac{1}{5}}[/latex]

Answer: Solution To convert a fraction to a decimal, divide the numerator by the denominator.

1.  [latex]{\Large\frac{3}{4}}[/latex]
Change to a decimal. .
Write as a percent by moving the decimal two places. [latex]75[/latex]%
2.  [latex]{\Large\frac{11}{8}}[/latex]
Change to a decimal. .
Write as a percent by moving the decimal two places. [latex]137.5[/latex]%
3.  [latex]2{\Large\frac{1}{5}}[/latex]
Write as an improper fraction. [latex]{\Large\frac{11}{5}}[/latex]
Change to a decimal. .
Write as a percent. [latex]220[/latex]%

Convert [latex]{\Large\frac{5}{7}}[/latex] to a percent.

Answer: Solution To change a fraction to a decimal, we divide the numerator by the denominator.

[latex]\Large\frac{5}{7}[/latex]
Change to a decimal—rounding to the nearest thousandth. [latex]0.714[/latex]
Write as a percent. [latex]71.4[/latex]%

Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right. Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.

try it

[ohm_question]146669[/ohm_question] [ohm_question]146670[/ohm_question] [ohm_question]146671[/ohm_question]
To summarize, here are the results from the previous example in a table.
Fraction Decimal Percent
[latex]{\Large\frac{3}{4}}[/latex] [latex]0.75[/latex] [latex]75[/latex]%
[latex]{\Large\frac{11}{8}}[/latex]  [latex]1.375[/latex] [latex]137.5[/latex]%
[latex]2{\Large\frac{1}{5}} ={\Large\frac{11}{5}}[/latex]  [latex]2.20[/latex] [latex]220[/latex]%
 

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  • Question ID 146671, 146670, 146669, 146668, 146667. Authored by: Lumen Learning. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

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