Changing a Percent to a Fraction or a Decimal

Transcription

1 6. Changing a Percent to a Fraction or a Decimal 6. OBJECTIVES. Use the percent notation 2. Change a percent to a fraction. Change a percent to a mixed number 4. Change a percent to a decimal When we considered parts of a whole in earlier chapters, we used fractions and decimals. The idea of percent is another useful way of naming parts of a whole. We can think of percents as ratios whose denominators are 00. In fact, the word percent means for each hundred. Look at the following drawing: The symbol for percent, %, represents multiplication by the number. In the drawing above, 25 of 00 squares are shaded. As a fraction, we write this as % 25 percent of the squares are shaded. Example Using Percent Notation (a) Four out of five geography students passed their midterm exams. Write this statement, using the percent notation. NOTE The ratio of students passing to students taking the 4 class is % Percent means for each hundred. To obtain a denominator of 00, multiply the numerator and denominator of the original fraction by 20. So we can say that 80% of the geography students passed. (b) Of 50 automobiles sold by a dealer in month, 5 were compact cars. Write this statement, using the percent notation. 200 McGraw-Hill Companies NOTE The ratio of compact 5 cars to all cars is % We can say that 70% of the cars sold were compact cars. CHECK YOURSELF Rewrite the following statement, using the percent notation: 4 of the 50 parts in a shipment were defective. 47

2 472 CHAPTER 6 PERCENTS Because there are different ways of naming the parts of a whole, you need to know how to change from one of these ways to another. First let s look at changing a percent to a fraction. Because a percent is a fraction or a ratio with denominator 00, we can use the following rule. Rules and Properties: Changing a Percent to a Fraction To change a percent to a common fraction, replace the percent symbol with 00. The use of this rule is shown in our first example. Example 2 Changing a Percent to a Fraction Change each percent to a fraction. (a) 7% NOTE You can choose to 25 reduce to simplest form. 00 (b) 25% CHECK YOURSELF 2 Write 2% as a fraction. If a percent is greater than 00, the resulting fraction will be greater than. This is shown in Example. Example Changing a Percent to a Mixed Number Change 50% to a mixed number. 50% CHECK YOURSELF Write 25% as a mixed number. 200 McGraw-Hill Companies

3 CHANGING A PERCENT TO A FRACTION OR A DECIMAL SECTION The fractional equivalents of certain percents should be memorized. % % It is best to try to remember these fractional equivalents. In Example 2, we wrote percents as fractions by replacing the percent sign with 00 and multiplying. How do we convert percents when we are working with decimals? Just move the decimal point two places to the left. This gives us a second rule for converting percents. Rules and Properties: Changing a Percent to a Decimal To change a percent to a decimal, replace the percent symbol with As a 00. result of multiplying by, the decimal point will move two places to the left. 00 Example 4 Changing a Percent to a Decimal Change each percent to a decimal equivalent. NOTE A percent greater than 00 gives a decimal greater than. (a) (b) 25% 8% (c) 0% The decimal point in 25% is understood to be after the 5. We must add a zero to move the decimal point. CHECK YOURSELF 4 (a) 5% (b) 2% (c) 5% Look at Example 5, which involves fractions of a percent. In this case, decimal fractions are involved. 200 McGraw-Hill Companies Example 5 Changing a Percent to a Decimal (a) 4.5% (b) 0.5%

4 474 CHAPTER 6 PERCENTS CHECK YOURSELF 5 (a) 8.5% (b) 0.% You will also find examples in which common fractions are involved in a percent. Example 6 illustrates this approach. Example 6 Changing a Percent to a Decimal NOTE Write the common fractions as decimals. Then remove the percent symbol by our earlier rule. 9 2 % 4 % 9.5% % CHECK YOURSELF 6 (a) 7 (b) 2 % 2 % CHECK YOURSELF ANSWERS. 8% were defective 2. 2% (a) 0.05; (b) 0.2; (c).5 5. (a) 0.085; (b) (a) 0.075; (b) McGraw-Hill Companies

5 Name 6. Exercises Section Date Use percents to name the shaded portion of each drawing.. 2. ANSWERS Rewrite each statement, using the percent notation. 5. Out of every 00 eligible people, 5 voted in a recent election. 6. You receive $5 in interest for every $00 saved for year. 7. Out of every 00 entering students, 74 register for English composition. 8. Of 00 people surveyed, 29 watched a particular sports event on television Out of 0 voters in a state, are registered as independents. 0. A dealer sold 9 of the 20 cars available during a -day sale.. Of 50 houses in a development, 27 are sold. 200 McGraw-Hill Companies 2. Of the 25 employees of a company, 9 are part-time.. Out of 50 people surveyed, 2 prefer decaffeinated coffee out of 20 college students work at part-time jobs. 5. Of the 20 students in an algebra class, 5 receive a grade of A. 475

6 ANSWERS Of the 50 families in a neighborhood, have children in public schools Write as fractions or mixed numbers. 7. 6% 8. 7% 9. 75% % 2. 65% % % % % % % 28. 4% % 0. 40% % % % 4. 70% 5. 5% % 7. 9% 8. 27% 9. 5% 40. 7% 4. 5% % % % 200 McGraw-Hill Companies 476

7 ANSWERS % % % 48..5% % % % Solve the following applications. 8 4 % Travel. Automobiles account for 85% of the travel between cities in the United States. What fraction does this percent represent? Travel. Automobiles and small trucks account for 84% of the travel to and from work in the United States. What fraction does this percent represent? 55. Explain the difference between of a quantity and of a quantity. 4 4 % 56. Match the percents in column A with their equivalent fractions in column B. 200 McGraw-Hill Companies Column A (a) 7 () 2 % (b) 5% (2) (c) () % (d) 8 (4) % (e) 60% (5) Column B (f) 62 (6) 2 %

8 ANSWERS Complete the chart for the percentages given in the bar graph. Nations Most Reliant on Nuclear Energy, 997 (Nuclear electricity generation as % of total) Lithuania France 8.5% 78.2% Belgium 60.% Ukraine Sweden Bulgaria Slovak Republic Switzerland Slovenia 46.8% 46.2% 45.4% 44% 40.6% 9.9% Hungary 9.9% Source: International Atomic Energy Agency, May 998 Country Fraction Equivalent Decimal Equivalent Lithuania France Belgium Ukraine Sweden Bulgaria Slovak Republic Switzerland Slovenia Hungary 58. The minimum daily values (MDV) for certain foods are given. They are based on a 2000 calorie per day diet. Find decimal and fractional notation for the percent notation in each sentence. 200 McGraw-Hill Companies 478

9 ANSWERS (a) ounce of Tostitos provides (b) cup of B & M baked beans 2 9% of the MDV of fat. contains 5% of the MDV of sodium. 58. (a) (b) (c) (d) (e) (f) (c) cup of Campbells New (d) 2 ounces of Star Kist tuna provide 2 27% of the MDV of protein. England clam chowder provides 6% of the MDV of iron. 59. (e) Four 4-in. Aunt Jemima pancakes provide % of the MDV of sodium. (f) 6 grams of Pop-Secret butter popcorn provides 2% of the MDV of sodium. 200 McGraw-Hill Companies 59. Convert the discount shown on the price tag to a decimal and fraction in lowest terms. 479

10 ANSWERS Convert the discount shown to a decimal and fraction in lowest terms. Answers. 5%. 75% 5. 5% of the eligible people voted % registered for English composition. 9. 0% are registered as independents.. 54% of the houses are sold.. 46% prefer decaffeinated coffee %; 25% of the students received As See table below ; Country Fraction Equivalent Decimal Equivalent Lithuania France Belgium Ukraine Sweden Bulgaria Slovak Republic Switzerland Slovenia Hungary McGraw-Hill Companies 480