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Percent - XYZ Custom Plus

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5.1 <strong>Percent</strong>s, Decimals, and Fractions307E Changing Fractions to <strong>Percent</strong>sTo change a fraction to a percent, we can change the fraction to a decimal andthen change the decimal to a percent.Example 24Suppose the price your bookstore pays for your textbookis ​_710 ​of the price you pay for your textbook. Write ​7 _​as a percent.10Solution We can change ​_7 ​to a decimal by dividing 7 by 10:100.7____10​) 7.0 ​7 0024. Change to a percent.a. ​_910 ​b. ​ 9 _20 ​We then change the decimal 0.7 to a percent by moving thedecimal point two places to the right and using the % symbol:0.7 = 70%You may have noticed that we could have saved some time in Example 24by simply writing ​_7 ​ as an equivalent fraction with denominator 100. That is:10_​ 7 ​= ​7_ ⋅ 10​= ​70_​= 70%10 10 ⋅ 10 100This is a good way to convert fractions like ​_7 ​to percents. It works well for fractionswith denominators of 2, 4, 5, 10, 20, 25, and 50, because they are easy to10change to fractions with denominators of 100.Example 25Change ​ 3 _​to a percent.8Solution We write ​_3 ​as a decimal by dividing 3 by 8. We then change the8decimal to a percent by moving the decimal point two places to the right andusing the % symbol.25. Change to a percent.a. ​_5 8 ​b. ​ 9 _8 ​_​ 3 ​= 0.375 = 37.5%8_____ .3758​) 3.000 ​2—460—564040 —026. Change to a percent.Example 26Change ​_5 ​to a percent.12Solution We begin by dividing 5 by 12:_______ .416612​) 5.0000 ​4 8201280728072a. ​ 7 _12 ​b. ​ 13 _12 ​Answers24. a. 90% b. 45%25. a. 62.5% b. 112.5%

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