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The figures shows two columns and five rows . The  first row is a header row and it labels each column “Percent” and “Decimal”. Under the “Percent” column are the values: 6%, 78%, 135%, 12.5%. Under the “Decimal” column are the values: 0.06, 0.78, 1.35, 0.125. There are two jumps for each percent to show how to convert it to a decimal.

Among a group of business leaders, 77% believe that poor math and science education in the U.S. will lead to higher unemployment rates.

Convert the percent to: a fraction a decimal

Solution

77%
Write as a ratio with denominator 100. 77 100
77 100
Change the fraction to a decimal by dividing the numerator by the denominator. 0.77
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Convert the percent to: a fraction and a decimal

Twitter's share of web traffic jumped 24% when one celebrity tweeted live on air.

  1. 6 25
  2. 0.24

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Convert the percent to: ⓐ a fraction andⓑ a decimal

The U.S. Census estimated that in 2013 , 44% of the population of Boston age 25 or older have a bachelor's or higher degrees.

  1. 22 50
  2. 0.44

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There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is 25% . Convert the percent to:

  1. ⓐ a fraction
  2. ⓑ a decimal

The figure shows someone holding a deck of cards.
(credit: Riles32807, Wikimedia Commons)

Solution

25%
Write as a ratio with denominator 100. 25 100
Simplify. 1 4
1 4
Change the fraction to a decimal by dividing the numerator by the denominator. 0.25
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Convert the percent to: a fraction, and a decimal

The probability that it will rain Monday is 30% .

  1. 3 10
  2. 0.3

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Convert the percent to: a fraction, and a decimal

The probability of getting heads three times when tossing a coin three times is 12.5% .

  1. 12.5 100
  2. 0.125

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Convert decimals and fractions to percents

To convert a decimal to a percent    , remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100 , 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 100 , rewrite it as an equivalent fraction with denominator 100 .
  3. Write this ratio as a percent.

Convert each decimal to a percent: 0.05 0.83

Solution

0.05
Write as a fraction. The denominator is 100. 5 100
Write this ratio as a percent. 5%
0.83
The denominator is 100. 83 100
Write this ratio as a percent. 83%
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Convert each decimal to a percent: 0.01 0.17 .

  1. 1%
  2. 17%

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Convert each decimal to a percent: 0.04 0.41

  1. 4%
  2. 41%

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To convert a mixed number to a percent, we first write it as an improper fraction.

Convert each decimal to a percent: 1.05 0.075

Solution

0.05
Write as a fraction. 1 5 100
Write as an improper fraction. The denominator is 100. 105 100
Write this ratio as a percent. 105%

Notice that since 1.05 > 1 , the result is more than 100%.

0.075
Write as a fraction. The denominator is 1,000. 75 1,000
Divide the numerator and denominator by 10, so that the denominator is 100. 7.5 100
Write this ratio as a percent. 7.5%
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Convert each decimal to a percent: 1.75 0.0825

  1. 175%
  2. 8.25%

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Convert each decimal to a percent: 2.25 0.0925

  1. 225%
  2. 9.25%

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Let's summarize the results from the previous examples in [link] so we can look for a pattern.

Decimal Percent
0.05 5%
0.83 83%
1.05 105%
0.075 7.5%

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.

[link] uses the decimal numbers in [link] and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the % sign.

Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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