10 CHAPTER R Review of Basic Concepts Percent, Fraction, and Decimal Equivalents 1%= 1 100 =0.01, 10%= 10 100 =0.10, 100%= 100 100 =1 For example, 73% means “73 per one hundred.” 73%= 73 100 = 0.73 Essentially, we are dropping the % symbol from 73% and dividing 73 by 100. Doing this moves the decimal point, which is understood to be after the 3, two places to the left. Writing 0.73 as a percent is the opposite process. 0.73 = 0.73 # 100%= 73% 100%= 1 Moving the decimal point two places to the right and attaching a % symbol gives the same result. EXAMPLE 12 Converting Percents and Decimals by Moving the Decimal Point Convert each percent to a decimal and each decimal to a percent. (a) 45% (b) 250% (c) 9% (d) 0.57 (e) 1.5 (f) 0.007 SOLUTION (a) 45%= 0.45 (b) 250%= 2.50, or 2.5 (c) 9%= 09%= 0.09 (d) 0.57 = 57% (e) 1.5 = 1.50 = 150% (f) 0.007 = 0.7% S Now Try Exercises 151 and 161. Converting Percents and Decimals (Shortcuts) • To convert a percent to a decimal, move the decimal point two places to the left and drop the % symbol. • To convert a decimal to a percent, move the decimal point two places to the right and attach a % symbol. Drop %. Divide by 100. (Move decimal point two places left.) Decimal Percent 0.85 85% Multiply by 100. Attach %. (Move decimal point two places right.) Percents as Decimals and Decimals as Percents The word percent means “per 100.” Percent is written with the symbol %. “One percent” means “one per one hundred,” or “one one-hundredth.” See Figure 7. Figure 7 35 of the 100 squares are shaded. That is, 35 100, or 35%, of the figure is shaded.
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