A fraction whose denominator is 100 is called a percent. The word percent means hundredths (per hundred).
Changing decimals to percents
To change decimals to percents,
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Move the decimal point two places to the right.
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Insert a percent sign.
Example 1
Change to percents.
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0.09 = 9%
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0.75 = 75%
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1.85 = 185%
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0.002 = 0.2%
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8.7 = 870%
Changing percents to decimals
To change percents to decimals,
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Eliminate the percent sign.
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Move the decimal point two places to the left (sometimes, adding zeros will be necessary).
Example 2
Change to decimals.
Changing fractions to percents
There are two simple methods for changing fractions to percents.
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Change to a decimal.
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Change the decimal to a percent.
24
Example 3
Change to percents.
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Make a proportion with the fraction on the left side of the equal sign and
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Solve the proportion for x, then place a % sign to its right.
24
Example 4
Change to percents.
Changing percents to fractions
There are two simple methods for changing percents to fractions.
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Drop the percent sign.
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Write over one hundred.
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Reduce if necessary.
25a
Example 5
Change to fractions.
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Drop the percent sign.
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Multiply by
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Reduce if necessary.
25b
Example 6
Change to fractions.
Memorizing the following can eliminate computations:
Finding the percent of a number
To determine the percent of a number, change the percent to a fraction or decimal (whichever is easier for you) and multiply. Remember, the word of means multiply.
Example 7
Find the percents of these numbers.
Other applications of percent
Turn the question word‐for‐word into an equation. For what, substitute the letter x; for is, substitute an equal sign; for of, substitute a multiplication sign. Change percents to decimals or fractions, whichever you find easier. Then solve the equation.
Example 8
Turn each of the following into an equation and solve.
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18 is what percent of 90?
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10 is 50 percent of what number?
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What is 15 percent of 60?
Percent—proportion method
Another simple method commonly used to solve percent problems is the proportion or is/of method. First set up a blank proportion and then fill in the empty spaces by using the following steps.
This method, using proportions with is/of, works for the three basic types of percent questions.
28a
Example 9
30 is what percent of 50?
The “is” number is 30. The % number is unknown, so call it x.
The “of” number is 50. Now replace these values in the appropriate positions in the proportion and solve for x.
In this particular instance, it can be observed that
28b
Example 10
30 is 20% of what number?
Therefore, 30 is 20% of 150.
28c
Example 11
What number is 30% of 50?
Therefore, 15 is 30% of 50.