6.1 Understand Percent

Learning Objectives

By the end of this section, you will be able to:

• Use the definition of percent
• Convert percents to fractions and decimals
• Convert decimals and fractions to percents

Use the Definition of Percent

How many cents are in one dollar? There are 100100 cents in a dollar. How many years are in a century? There are 100100 years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A percent is a ratio whose denominator is 100. We use the percent symbol %, to show percent.

According to data from the American Association of Community Colleges (2015), about 57% of community college students are female. This means 57 out of every 100 community college students are female, as Figure 6.2 shows. Out of the 100 squares on the grid, 57 are shaded, which we write as the ratio 57100.

Figure 6.2 Among every 100100 community college students, 5757 are female.

Similarly, 25% means a ratio of 25/100,3% means a ratio of 3100 and 100% means a ratio of 100/100 . In words, “one hundred percent” means the total 100% is 100/100, and since 100/100=1, we see that 100% means 1 whole.

Convert Percents to Fractions and Decimals

Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per 100, so the denominator of the fraction is 100

The previous example shows that a percent can be greater than 1. We saw that 125% means 125/100, or 5/4. These are improper fractions, and their values are greater than one.

In Decimals, we learned how to convert fractions to decimals. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.

Let’s summarize the results from the previous examples in Table 6.1, and look for a pattern we could use to quickly convert a percent number to a decimal number.

Percent	Decimal
6%	0.06
78%	0.78
135%	1.35
12.5%	0.125

Table6.1

Do you see the pattern?

To convert a percent number to a decimal number, we move the decimal point two places to the left and remove the %% sign. (Sometimes the decimal point does not appear in the percent number, but just like we can think of the integer 6 as 6.0, we can think of 6% as 6.0%.) Notice that we may need to add zeros in front of the number when moving the decimal to the left.

Figure 6.3 uses the percents in Table 6.1 and shows visually how to convert them to decimals by moving the decimal point two places to the left.

Figure 6.3

Convert Decimals and Fractions to Percents

To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100,  it is easy to change that fraction to a percent.

Let’s summarize the results from the previous examples in Table 6.2 so we can look for a pattern.

Decimal	Percent
0.05	5%
0.83	83%
1.05	105%
0.075	7.5%

Table6.2

Do you see the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.

Figure 6.5 uses the decimal numbers in Table 6.2 and shows visually to convert them to percents by moving the decimal point two places to the right and then writing the %% sign.

Figure 6.5

In Decimals, we learned how to convert fractions to decimals. Now we also know how to change decimals to percents. So to convert a fraction to a percent, we first change it to a decimal and then convert that decimal to a percent.

Sometimes when changing a fraction to a decimal, the division continues for many decimal places and we will round off the quotient. The number of decimal places we round to will depend on the situation. If the decimal involves money, we round to the hundredths place. For most other cases in this book we will round the number to the nearest thousandth, so the percent will be rounded to the nearest tenth.

When we first looked at fractions and decimals, we saw that fractions converted to a repeating decimal. When we converted the fraction 43 to a decimal, we wrote the answer as 1.3¯. We will use this same notation, as well as fraction notation, when we convert fractions to percents in the next example.

Section 6.1 Exercises

Practice Makes Perfect

Use the Definition of Percents

In the following exercises, write each percent as a ratio.

1. In 2014, the unemployment rate for those with only a high school degree was 6.0%.
2. In 2015, among the unemployed, 29% were long-term unemployed.
3. The unemployment rate for those with Bachelor’s degrees was 3.2% in 2014.
4. The unemployment rate in Michigan in 2014 was 7.3%.
   In the following exercises, write as

ⓐ a ratio and
ⓑ a percent

5. 57 out of 100 nursing candidates received their degree at a community college.
6. 80 out of 100 firefighters and law enforcement officers were educated at a community college.
7. 42 out of 100 first-time freshmen students attend a community college.
8. 71 out of 100 full-time community college faculty have a master’s degree.
   Convert Percents to Fractions and Decimals

In the following exercises, convert each percent to a fraction and simplify all fractions.

9. 4%
10. 8%
11. 17%
12. 19%
13. 52%
14. 78%
15. 125%
16. 135%
17. 37.5%
18. 42.5%
19. 18.4%
20. 46.4%
21. 912%
22. 812%
23. 513%
24. 623%
    In the following exercises, convert each percent to a decimal.
25. 5%
26. 9%
27. 1%
28. 2%
29. 63%
30. 71%
31. 40%
32. 50%
33. 115%
34. 125%
35. 150%
36. 250%
37. 21.4%
38. 39.3%
39. 7.8%
40. 6.4%
    In the following exercises, convert each percent to

ⓐ a simplified fraction and
ⓑ a decimal

41. In 2010,1.5% of home sales had owner financing. (Source: Bloomberg Businessweek, 5/23–29/2011)
42. In 2000,4.2% of the United States population was of Asian descent. (Source: www.census.gov)
43. According to government data, in 2013 the number of cell phones in India was 70.23% of the population.
44. According to the U.S. Census Bureau, among Americans age 25 or older who had doctorate degrees in 2014,37.1% are women.
45. A couple plans to have two children. The probability they will have two girls is 25%.
46. Javier will choose one digit at random from 0 through 9. The probability he will choose 3 is 10%.
47. According to the local weather report, the probability of thunderstorms in New York City on July 15 is 60%.
48. A club sells 50 tickets to a raffle. Osbaldo bought one ticket. The probability he will win the raffle is 2%.
    Convert Decimals and Fractions to Percents

In the following exercises, convert each decimal to a percent.

49. 0.01
50. 0.03
51. 0.18
52. 0.15
53. 1.35
54. 1.56
55. 3
56. 4
57. 0.009
58. 0.008
59. 0.0875
60. 0.0625
61. 1.5
62. 2.2
63. 2.254
64. 2.317
    In the following exercises, convert each fraction to a percent.
65. 14
66. 15
67. 38
68. 58
69. 74
70. 98
71. 645
72. 514
73. 512
74. 1112
75. 223
76. 123
77. 37
78. 67
79. 59
80. 49
    In the following exercises, convert each fraction to a percent.
81. 14 of washing machines needed repair.
82. 15 of dishwashers needed repair.
    In the following exercises, convert each fraction to a percent.
83. According to the National Center for Health Statistics, in 2012,720 of American adults were obese.
84. The U.S. Census Bureau estimated that in 2013,85% of Americans lived in the same house as they did 1 year before.
    In the following exercises, complete the table.

Everyday Math

87. 

Sales tax Felipa says she has an easy way to estimate the sales tax when she makes a purchase. The sales tax in her city is 9.05%. She knows this is a little less than 10%.

ⓐ Convert 10% to a fraction.
ⓑ Use your answer from ⓐ to estimate the sales tax Felipa would pay on a $95 dress.

88. Savings Ryan has 25% of each paycheck automatically deposited in his savings account.
    ⓐ Write 25% as a fraction.
    ⓑ Use your answer from ⓐ to find the amount that goes to savings from Ryan’s $2,400 paycheck.
    Amelio is shopping for textbooks online. He found three sellers that are offering a book he needs for the same price, including shipping. To decide which seller to buy from he is comparing their customer satisfaction ratings. The ratings are given in the chart.

Use the chart to answer the following questions

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.