11 R.1 Fractions, Decimals, and Percents A number greater than 1 is more than 100%. SOLUTION (a) We use the fact that percent means “per one hundred,” and convert as follows. 8%= 8 100 = 2 # 4 25 # 4 = 2 25 As with converting percents to decimals, drop the % symbol and divide by 100. Write in lowest terms. (b) 175%= 175 100 = 7 # 25 4 # 25 = 7 4 , or 1 3 4 Write in lowest terms. (c) 13.5% = 13.5 100 Drop the % symbol. Divide by 100. = 13.5 100 # 10 10 Multiply by 1 in the form 10 10 to eliminate the decimal in the numerator. = 135 1000 Multiply. = 27 200 Write in lowest terms. 135 1000 = 27 # 5 200 # 5 = 27 200 S Now Try Exercises 171, 177, and 179. EXAMPLE 13 Writing Percents as Fractions Write each percent as a fraction. Give answers in lowest terms. (a) 8% (b) 175% (c) 13.5% Percents as Fractions and Fractions as Percents EXAMPLE 14 Writing Fractions as Percents Write each fraction as a percent. (a) 2 5 (b) 1 6 SOLUTION (a) 2 5 = 2 5 # 100% Multiply by 1 in the form 100%. = 2 5 # 100 1 % = 2 # 5 # 20 5 # 1 % Multiply and factor. = 2 # 20 1 % Divide out the common factor. = 40% Simplify. (b) 1 6 S Now Try Exercises 181 and 185. = 1 6 # 100% = 1 6 # 100 1 % = 1 # 2 # 50 2 # 3 # 1 % = 50 3 % = 16 2 3 %, or 16.6%
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