1. science
2. mathematics
3. arithmetic

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