© 2001 McGraw-Hill Companies 471
Changing a Percent to a
Fraction or a Decimal
6.1
6.1 OBJECTIVES1. Use the percent notation 2. Change a percent to a fraction 3. Change a percent to a mixed number 4. Change a percent to a decimal
NOTE The ratio of students passing to students taking the class is .4
5
Example 1
Using Percent Notation
(a) Four out of five geography students passed their midterm exams. Write this statement, using the percent notation.
So we can say that 80% of the geography students passed.
(b) Of 50 automobiles sold by a dealer in 1 month, 35 were compact cars. Write this statement, using the percent notation.
We can say that 70% of the cars sold were compact cars. 35 50 70 100 70
1 100 70%Percent means for each hundred. To obtain a denominator of 100, multiply the numerator and denominator of the original fraction by 20.
4 5 80 100 80
1 100 80% C H E C K Y O U R S E L F 1Rewrite the following statement, using the percent notation: 4 of the 50 parts in a shipment were defective.
NOTEThe ratio of compact cars to all cars is 35.
50
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 per-cents as ratios whose denominators are 100. In fact, the word percent means “for each hun-dred.” Look at the following drawing:
The symbol for percent, %, represents multiplication by the number . In the drawing above, 25 of 100 squares are shaded. As a fraction, we write this as .
25 percent of the squares are shaded. 25 100 25
1 100 25% 25 100 1 100472 CHAPTER6 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.
© 2001 McGraw-Hill Companies
To change a percent to a common fraction, replace the percent symbol with 1
100.
Rules and Properties: Changing a Percent to a Fraction
The use of this rule is shown in our first example.
Example 2
Example 3
Changing a Percent to a Fraction Change each percent to a fraction.
(a) (b) 25
1 100 25 100 1 4 25% 7 1 100 7 100 7%NOTEYou can choose to reduce 25 to simplest form.
100
C H E C K Y O U R S E L F 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.
Changing a Percent to a Mixed Number Change 150% to a mixed number.
150
1 100 150 100 1 50 100 1 1 2 150% C H E C K Y O U R S E L F 3The 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 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. 1 100 662 3% 66 2 3 1 100 200 3 1 100 2 3 331 3% 33 1 3
1 100 100 3 1 100 1 3 © 2001 McGraw-Hill CompaniesNOTEA percent greater than 100 gives a decimal greater than 1.
To change a percent to a decimal, replace the percent symbol with As a result of multiplying by 1 , the decimal point will move two places to the left.
100
1 100. Rules and Properties: Changing a Percent to a Decimal
Example 4
Changing a Percent to a Decimal Change each percent to a decimal equivalent.
(a) (b) (c) 130
1 100 1.30 130% 8 1 100 0.08 8%The decimal point in 25% is understood to be after the 5.
We must add a zero to move the decimal point.
25
1 100 0.25 25% C H E C K Y O U R S E L F 4 Write as decimals. (a) 5% (b) 32% (c) 115%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)
(b) 0.5% 0.5
1001 0.005 4.5 1001 0.045 4.5%474 CHAPTER6 PERCENTS
You will also find examples in which common fractions are involved in a percent. Example 6 illustrates this approach.
© 2001 McGraw-Hill Companies
C H E C K Y O U R S E L F 5
Write as decimals.
(a) 8.5% (b) 0.3%
Example 6
Changing a Percent to a Decimal Write as decimals. 0.75% 0.75
1001 0.0075 3 4% 9.5% 9.5 1 100 0.095 91 2%NOTEWrite the common fractions as decimals. Then remove the percent symbol by our earlier rule.
C H E C K Y O U R S E L F A N S W E R S
1. 8% were defective 2. 3. 4. (a) 0.05; (b) 0.32; (c) 1.15 5. (a) 0.085; (b) 0.003 6. (a) 0.075; (b) 0.005 11 4 12% 12 100 3 25 C H E C K Y O U R S E L F 6 Write as decimals. (a) (b) 1 2% 71 2%
© 2001 McGraw-Hill Companies
Exercises
Use percents to name the shaded portion of each drawing.
1. 2.
3. 4.
Rewrite each statement, using the percent notation.
5. Out of every 100 eligible people, 53 voted in a recent election.
6. You receive $5 in interest for every $100 saved for 1 year.
7. Out of every 100 entering students, 74 register for English composition.
8. Of 100 people surveyed, 29 watched a particular sports event on television.
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.
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.
6.1
Section Date ANSWERS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 475© 2001 McGraw-Hill Companies 16. Of the 50 families in a neighborhood, 31 have children in public schools.
Write as fractions or mixed numbers.
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. 32. Write as decimals. 33. 20% 34. 70% 35. 35% 36. 75% 37. 39% 38. 27% 39. 5% 40. 7% 41. 135% 42. 250% 43. 240% 44. 160% 1331 3% 1662 3% ANSWERS 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 476
45. 23.6% 46. 10.5% 47. 6.4%
48. 3.5% 49. 0.2% 50. 0.5%
51. 52.
Solve the following applications.
53. Travel. Automobiles account for 85% of the travel between cities in the United States. What fraction does this percent represent?
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 of a quantity and of a quantity.
56. Match the percents in column A with their equivalent fractions in column B. Column A Column B (a) (1) (b) 5% (2) (c) (3) (d) (4) (e) 60% (5) (f ) (6) 1 3 621 2% 5 6 3 8 831 3% 1 20 331 3% 5 8 3 5 371 2% 1 4% 1 4 81 4% 71 2% © 2001 McGraw-Hill Companies 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 477
© 2001 McGraw-Hill Companies 57. Complete the chart for the percentages given in the bar graph.
0 20
Nations Most Reliant on Nuclear Energy, 1997 (Nuclear electricity generation as % of total) Lithuania France Belgium Ukraine Sweden Bulgaria Slovak Republic Switzerland Slovenia Hungary 10 30 40 50 60 70 80 90 100 81.5% 78.2% 60.1% 46.8% 46.2% 45.4% 44% 40.6% 39.9% 39.9%
Source: International Atomic Energy Agency, May 1998
ANSWERS
57.
478
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.
(a) 1 ounce of Tostitos provides (b) cup of B & M baked beans
9% of the MDV of fat. contains 15% of the MDV of sodium.
(c) cup of Campbells’ New (d) 2 ounces of Star Kist tuna provide England clam chowder 27% of the MDV of protein. provides 6% of the MDV of iron.
(e) Four 4-in. Aunt Jemima (f ) 36 grams of Pop-Secret butter popcorn pancakes provide 33% of provides 2% of the MDV of sodium. the MDV of sodium.
59. Convert the discount shown on the price tag to a decimal and fraction in lowest terms. 1 2 1 2 © 2001 McGraw-Hill Companies 58. (a) (b) (c) (d) (e) (f) 59. 479
© 2001 McGraw-Hill Companies 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.
15. 17. 19.
21. 23. 25. 27. 29. 31. 33. 0.2
35. 0.35 37. 0.39 39. 0.05 41. 1.35 43. 2.4 45. 0.236 47. 0.064 49. 0.002 51. 0.075 53. 55.
57. See table below 59. 0.15; 3 20 17 20 12 3 11 2 33 50 23 50 1 2 13 20 3 4 3 50 5 20 25
100 25%; 25% of the students received As.
ANSWERS
60.
480
Country Fraction Equivalent Decimal Equivalent
Lithuania .815 France .782 Belgium .601 Ukraine .468 Sweden .462 Bulgaria .454 Slovak Republic .440 Switzerland .406 Slovenia .399 Hungary 399 .399 1000 399 1000 203 500 11 25 227 500 231 500 117 250 601 1000 391 500 163 200
