6.1 Changing a Percent to a Fraction or a Decimal 6.1 OBJECTIVES 1. 2. 3. 4. Use the percent notation Change a percent to a fraction Change a percent to a mixed number 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 100. In fact, the word percent means “for each hundred.” Look at the following drawing: 1 . In the drawing 100 25 above, 25 of 100 squares are shaded. As a fraction, we write this as . 100 1 25 25 25% 100 100 The symbol for percent, %, represents multiplication by the number 25 percent of the squares are shaded. Example 1 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 . 5 4 80 1 80 80% 5 100 100 Percent means for each hundred. To obtain a denominator of 100, multiply the numerator and denominator of the original fraction by 20. So we can say that 80% of the geography students passed. © 2001 McGraw-Hill Companies (b) Of 50 automobiles sold by a dealer in 1 month, 35 were compact cars. Write this statement, using the percent notation. NOTE The ratio of compact 35 cars to all cars is . 50 70 1 35 70 70% 50 100 100 We can say that 70% of the cars sold were compact cars. CHECK YOURSELF 1 Rewrite the following statement, using the percent notation: 4 of the 50 parts in a shipment were defective. 471 472 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 100, 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 1 with . 100 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% 7 reduce 1 (b) 25% 25 25 to simplest form. 100 7 100 100 4 1 25 1 CHECK YOURSELF 2 Write 12% as a fraction. If a percent is greater than 100, the resulting fraction will be greater than 1. This is shown in Example 3. Example 3 Changing a Percent to a Mixed Number Change 150% to a mixed number. 150% 150 100 100 1100 12 1 150 CHECK YOURSELF 3 Write 125% as a mixed number. 50 1 © 2001 McGraw-Hill Companies NOTE You can choose to 100 100 CHANGING A PERCENT TO A FRACTION OR A DECIMAL SECTION 6.1 473 The fractional equivalents of certain percents should be memorized. 1 1 1 100 1 1 33 % 33 3 3 100 3 100 3 2 1 200 1 2 2 66 % 66 3 3 100 3 100 3 It is best to try to remember these fractional equivalents. 1 In Example 2, we wrote percents as fractions by replacing the percent sign with 100 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 1 . As a To change a percent to a decimal, replace the percent symbol with 100 1 result of multiplying by , the decimal point will move two places to the left. 100 Example 4 Changing a Percent to a Decimal Change each percent to a decimal equivalent. (a) 25% 25 (b) 8% 8 NOTE A percent greater than 100 gives a decimal greater than 1. 100 0.25 1 The decimal point in 25% is understood to be after the 5. 100 0.08 1 (c) 130% 130 We must add a zero to move the decimal point. 100 1.30 1 CHECK YOURSELF 4 Write as decimals. (a) 5% (b) 32% (c) 115% © 2001 McGraw-Hill Companies Look at Example 5, which involves fractions of a percent. In this case, decimal fractions are involved. Example 5 Changing a Percent to a Decimal Write as decimals. (a) 4.5% 4.5 100 0.045 (b) 0.5% 0.5 100 0.005 1 1 474 CHAPTER 6 PERCENTS CHECK YOURSELF 5 Write as decimals. (a) 8.5% (b) 0.3% 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 Write as decimals. fractions as decimals. Then remove the percent symbol by our earlier rule. 1 1 0.095 9 % 9.5% 9.5 100 2 1 3 0.0075 % 0.75% 0.75 100 4 CHECK YOURSELF 6 Write as decimals. 1 (a) 7 % 2 (b) 1 % 2 CHECK YOURSELF ANSWERS 1. 8% were defective (c) 1.15 2. 12% 5. (a) 0.085; (b) 0.003 12 3 1 3. 1 4. (a) 0.05; (b) 0.32; 100 25 4 6. (a) 0.075; (b) 0.005 © 2001 McGraw-Hill Companies NOTE Write the common Name 6.1 Exercises Section Date Use percents to name the shaded portion of each drawing. 1. 2. ANSWERS 1. 2. 3. 4. 3. 4. 5. 6. 7. 8. Rewrite each statement, using the percent notation. 5. Out of every 100 eligible people, 53 voted in a recent election. 9. 10. 11. 6. You receive $5 in interest for every $100 saved for 1 year. 12. 7. Out of every 100 entering students, 74 register for English composition. 13. 14. 8. Of 100 people surveyed, 29 watched a particular sports event on television. 15. 9. Out of 10 voters in a state, 3 are registered as independents. 10. A dealer sold 9 of the 20 cars available during a 1-day sale. © 2001 McGraw-Hill Companies 11. Of 50 houses in a development, 27 are sold. 12. Of the 25 employees of a company, 9 are part-time. 13. Out of 50 people surveyed, 23 prefer decaffeinated coffee. 14. 17 out of 20 college students work at part-time jobs. 15. Of the 20 students in an algebra class, 5 receive a grade of A. 475 ANSWERS 16. 16. Of the 50 families in a neighborhood, 31 have children in public schools. 17. 18. 19. 20. 21. Write as fractions or mixed numbers. 22. 17. 6% 18. 17% 19. 75% 20. 20% 21. 65% 22. 48% 23. 50% 24. 52% 25. 46% 26. 35% 27. 66% 28. 4% 29. 150% 30. 140% 31. 166 % 33. 20% 34. 70% 35. 35% 36. 75% 37. 39% 38. 27% 39. 5% 40. 7% 41. 135% 42. 250% 43. 240% 44. 160% 23. 24. 25. 26. 27. 28. 29. 30. 2 3 1 3 32. 133 % 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 476 © 2001 McGraw-Hill Companies Write as decimals. ANSWERS 45. 23.6% 46. 10.5% 47. 6.4% 45. 46. 48. 3.5% 49. 0.2% 1 51. 7 % 2 1 52. 8 % 4 50. 0.5% 47. 48. 49. 50. Solve the following applications. 53. Travel. Automobiles account for 85% of the travel between cities in the United 51. States. What fraction does this percent represent? 52. 53. 54. 55. 56. 54. 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 1 1 of a quantity and % of a quantity. 4 4 56. Match the percents in column A with their equivalent fractions in column B. Column A 1 (a) 37 % 2 © 2001 McGraw-Hill Companies (b) 5% 1 (c) 33 % 3 1 (d) 83 % 3 (e) 60% 1 (f) 62 % 2 Column B 3 (1) 5 5 (2) 8 1 20 3 (4) 8 5 (5) 6 (3) (6) 1 3 477 ANSWERS 57. 57. Complete the chart for the percentages given in the bar graph. Nations Most Reliant on Nuclear Energy, 1997 (Nuclear electricity generation as % of total) 81.5% Lithuania 78.2% France 60.1% Belgium Ukraine 46.8% Sweden 46.2% Bulgaria 45.4% 44% Slovak Republic Switzerland 40.6% Slovenia 39.9% 39.9% Hungary 0 10 20 30 40 50 60 70 80 90 100 Source: International Atomic Energy Agency, May 1998 Country Fraction Equivalent Decimal Equivalent Lithuania France Belgium Ukraine Sweden Bulgaria Slovak Republic 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. 478 © 2001 McGraw-Hill Companies Switzerland ANSWERS (a) 1 ounce of Tostitos provides 9% of the MDV of fat. (b) 1 cup of B & M baked beans 2 contains 15% of the MDV of sodium. 58. (a) (b) (c) (d) (e) (f) (c) 1 cup of Campbells’ New 2 England clam chowder provides 6% of the MDV of iron. © 2001 McGraw-Hill Companies (e) Four 4-in. Aunt Jemima pancakes provide 33% of the MDV of sodium. (d) 2 ounces of Star Kist tuna provide 27% of the MDV of protein. 59. (f) 36 grams of Pop-Secret butter popcorn provides 2% of the MDV of sodium. 59. Convert the discount shown on the price tag to a decimal and fraction in lowest terms. 479 ANSWERS 60. 60. Convert the discount shown to a decimal and fraction in lowest terms. Answers 1. 35% 3. 75% 5. 53% of the eligible people voted. 7. 74% registered for English composition. 9. 30% are registered as independents. 11. 54% of the houses are sold. 13. 46% prefer decaffeinated coffee. 5 25 3 3 25%; 25% of the students received As. 17. 19. 20 100 50 4 13 1 23 33 1 2 21. 23. 25. 27. 29. 1 31. 1 33. 0.2 20 2 50 50 2 3 35. 0.35 37. 0.39 39. 0.05 41. 1.35 43. 2.4 45. 0.236 17 47. 0.064 49. 0.002 51. 0.075 53. 55. 20 3 57. See table below 59. 0.15; 20 15. Lithuania France Belgium Ukraine Sweden Bulgaria Slovak Republic Switzerland Slovenia Hungary 480 Fraction Equivalent 163 200 391 500 601 1000 117 250 231 500 227 500 11 25 203 500 399 1000 399 1000 Decimal Equivalent .815 .782 .601 .468 .462 .454 .440 .406 .399 .399 © 2001 McGraw-Hill Companies Country

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