586 CHAPTER 10 Consumer Mathematics This procedure has the effect of converting the fraction to a decimal number and then moving the decimal point in the decimal number two places to the right and adding a percent sign. Note that Steps 2 and 3 together are the equivalent of multiplying by 100%. Since 100% 100/100 1, = = we are not changing the value of the decimal number—we are simply changing the decimal number to a percent. Example 1 Converting Fractions to Percents Change each of the following fractions to a percent. a) 67 100 b) 11 20 c) 15 16 Now try Exercise 7 MATHEMATICS TODAY Percent Versus Percentage When should the word percent be used and when should the word percentage be used? Although writing style manuals are not always consistent on the use of these words, a general rule is given below. • Percent (or the symbol %) accompanies a specific number. The word percent may also be used when a question is seeking a specific percent. Example 1—Eighty percent of the people liked the movie. Example 2—More than 80% (or 80 percent) of the boxes weighed more than 1 pound. Example 3—If a worker’s salary increased from $35,000 to $38,000 what is the percent increase? • Percentage is used without a specific number. Example 4—A large percentage of the population has had their flu shot. Example 5—The percentage of the population that has been exposed to the virus is between 60% and 70%. Some style manuals state that the word percent can be used in place of the word percentage on tables and graphs, and other places where space is limited. Also, in the United States, percent is usually written as one word, but in Europe and elsewhere it is often written using two words, percent. Note, too, that when writing a percent at the beginning of a sentence, as in Example 1 in this Mathematics Today box above, the words should be written out. Why This Is Important This information may be helpful if you need to write reports for school or for your job. In future examples, when changing a fraction to a percent, we will follow the three-step procedure given previously without listing the individual steps. We will do this in Example 4. To change a decimal number to a percent, use the following procedure. Solution For each fraction, follow the three steps given previously. a) 1. 67 100 0.67 ÷ = 2. 0.67 100 67 × = 3. 67% Thus, 67 100 67%. = a) 1. 11 20 0.55 ÷ = 2. 0.55 100 55 × = 3. 55% Thus, 11 20 55%. = a) 1. 15 16 0.9375 ÷ = 2. 0.9375 100 93.75 × = 3. 93.75% Thus, 15 16 93.75%. = 7 CHANGING DECIMAL NUMBERS TO PERCENTS 1. Multiply the decimal number by 100. 2. Add a percent sign. PROCEDURE The procedure for changing a decimal number to a percent is equivalent to moving the decimal point two places to the right and adding a percent sign. Example 2 Converting Decimal Numbers to Percents Change each of the following decimal numbers to a percent. a) 0.14 b) 0.893 c) 0.7625 Solution a) 0.14 (0.14 100)% 14%. = × = Thus, 0.14 14%. = b) 0.893 (0.893 100)% 89.3%. = × = Thus, 0.893 89.3%. = c) 0.7625 (0.7625 100)% 76.25%. = × = Thus, 0.7625 76.25%. = 7 Now try Exercise 11 CHANGING PERCENTS TO DECIMAL NUMBERS 1. Remove the percent sign. 2. Divide the number by 100. PROCEDURE To change a number given as a percent to a decimal number, follow this procedure.
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