10.1 Percent 585 The weather app on your phone says that there is a 75% chance of rain. Based on this information, you decide to carry your umbrella. In this section, we will investigate the meaning of percent and learn how percents relate to mathematics and to daily life. Percent SECTION 10.1 LEARNING GOALS Upon completion of this section, you will be able to: 7 Convert between a percent, a fraction, and a decimal number. 7 Solve problems involving percent change. 7 Solve problems involving percent markup and markdown. 7 Solve other percent problems. Why This Is Important Many decisions that we make every day involve applications of percent. An understanding of percent is essential in making informed decisions. For example, if we need to determine how much a meal will cost including tax and tip, we need an understanding of percent. Recall from Chapter 6 that financial literacy refers to the ability to make smart, informed decisions regarding the management of money. Understanding how to work with percent, fractions, and decimal numbers is an important part of financial literacy and consumer mathematics. Percent, Fractions, and Decimal Numbers A basic topic necessary for understanding the material in this chapter is percent. The word percent comes from the Latin per centum, meaning “per hundred.” A percent is simply a ratio of some number to 100. Thus, 15%, 15 100 = and x%. x 100 = Percents are useful in making comparisons. Consider Ross, who took two chemistry tests. On the first test Ross answered 18 of the 20 questions correctly, and on the second test he answered 23 of 25 questions correctly. On which test did he have the higher score? One way to compare the results is to write ratios of the number of correct answers to the number of questions on the test and then convert the ratios to percents. We can determine the grades in percent for each test by (a) writing a ratio of the number of correct answers to the total number of questions, (b) rewriting these ratios with a denominator of 100, and (c) expressing the ratios as percents. Test 1 (a) (b) (c) = = × × = = = = × × = = Number of correct answers Number of questions on the test 18 20 18 5 20 5 90 100 90% Number of correct answers Number of questions on the test 23 25 23 4 25 4 92 100 92% Test 2 (a) (b) (c) By changing the results of both tests to percents, we have a common standard for comparison. The results show that Ross scored 90% on the first test and 92% on the second test. Thus, he had a higher score on the second test. Another procedure to change a fraction to a percent follows. CHANGING FRACTIONS TO PERCENTS 1. Divide the numerator by the denominator to obtain a decimal number. 2. Multiply the decimal number by 100 (which has the effect of moving the decimal point two places to the right). 3. Add a percent sign. PROCEDURE Ollyy/Shutterstock
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