3.2 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 cents in a dollar. How many years are in a century? There are
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
. We use the percent symbol
to show percent.
Percent
A percent is a ratio whose denominator is .
According to data from the Statistics Canada, of Canadian Internet users reported a cyber security incident, including being redirected to fraudulent websites that asked for personal information or getting a virus or other computer infection. This means
out of every
Canadian internet users reported cyber security incidents as (Figure 1) shows. Out of the
squares on the grid,
are shaded, which we write as the ratio
.

Similarly, means a ratio of
means a ratio of
and
means a ratio of
. In words, “one hundred percent” means the total
is
, and since
, we see that
means
whole.
EXAMPLE 1
According to a survey done by Universities Canada of Canada’s Universities are working to include Indigenous representation within their governance or leadership structures.Write this percent as a ratio.
The amount we want to convert is 71%. | ![]() |
Write the percent as a ratio. Remember that percent means per 100. | ![]() |
TRY IT 1.1
Write the percent as a ratio.
According to a survey, of college students have a smartphone.
Answer
TRY IT 1.2
Write the percent as a ratio.
A study found that of Canadian teens send text messages regularly.
Answer
EXAMPLE 2
In , according to a Universities Canada survey,
out of every
of today’s undergraduates benefit from experiential learning such as co-ops, internships and service learning. Write this as a ratio and then as a percent.
The amount we want to convert is ![]() ![]() |
![]() ![]() |
Write as a ratio. | ![]() |
Convert the 56 per 100 to percent. | ![]() |
TRY IT 2.1
Write as a ratio and then as a percent: According to Statistics Canada, only out of
young Canadians cross a provincial border to complete their university degree.
Answer
TRY IT 2.2
Write as a ratio and then as a percent: According to an international comparison done by the British Council, out of
current professional leaders across 30 countries and in all sectors, are liberal arts grads with bachelor’s degrees in the social sciences or humanities.
Answer
Convert Percents to Fractions and Decimals
Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per , so the denominator of the fraction is
.
Convert a Percent to a Fraction.
- Write the percent as a ratio with the denominator
.
- Simplify the fraction if possible.
EXAMPLE 3
Convert each percent to a fraction:
a) | ![]() |
b) | ![]() |
|
Write as a ratio with denominator 100. | ![]() |
Write as a ratio with denominator 100. | ![]() |
|
Simplify. | ![]() |
Simplify. | ![]() |
TRY IT 3.1
Convert each percent to a fraction:
Answer
TRY IT 3.2
Convert each percent to a fraction:
Answer
The previous example shows that a percent can be greater than . We saw that
means
, or
. These are improper fractions, and their values are greater than one.
EXAMPLE 4
Convert each percent to a fraction:
a) | ![]() |
Write as a ratio with denominator 100. | ![]() |
Clear the decimal by multiplying numerator and denominator by 10. | ![]() |
Multiply. | ![]() |
Rewrite showing common factors. | ![]() |
Simplify. | ![]() |
b) | ![]() |
Write as a ratio with denominator 100. | ![]() |
Write the numerator as an improper fraction. | ![]() |
Rewrite as fraction division, replacing 100 with ![]() |
![]() |
Multiply by the reciprocal. | ![]() |
Simplify. | ![]() |
TRY IT 4.1
Convert each percent to a fraction:
Answer
TRY IT 4.2
Convert each percent to a fraction:
Answer
To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal.
HOW TO: Convert a Percent to a Decimal
- Write the percent as a ratio with the denominator
.
- Convert the fraction to a decimal by dividing the numerator by the denominator.
EXAMPLE 5
Convert each percent to a decimal:
Because we want to change to a decimal, we will leave the fractions with denominator instead of removing common factors.
a) | ![]() |
Write as a ratio with denominator 100. | ![]() |
Change the fraction to a decimal by dividing the numerator by the denominator. | ![]() |
b) | ![]() |
Write as a ratio with denominator 100. | ![]() |
Change the fraction to a decimal by dividing the numerator by the denominator. | ![]() |
TRY IT 5.1
Convert each percent to a decimal:
Answer
- 0.09
- 0.87
TRY IT 5.2
Convert each percent to a decimal:
Answer
- 0.03
- 0.91
EXAMPLE 6
Convert each percent to a decimal:
a) | ![]() |
Write as a ratio with denominator 100. | ![]() |
Change the fraction to a decimal by dividing the numerator by the denominator. | ![]() |
b) | ![]() |
Write as a ratio with denominator 100. | ![]() |
Change the fraction to a decimal by dividing the numerator by the denominator. | ![]() |
TRY IT 6.1
Convert each percent to a decimal:
Answer
- 1.15
- 0.235
TRY IT 6.2
Convert each percent to a decimal:
Answer
- 1.23
- 0.168
Let’s summarize the results from the previous examples in the table below, and look for a pattern we could use to quickly convert a percent number to a decimal number.
Percent | Decimal |
---|---|
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
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
as
, we can think of
as
.) Notice that we may need to add zeros in front of the number when moving the decimal to the left.
(Figure 2) uses the percents in the table above and shows visually how to convert them to decimals by moving the decimal point two places to the left.

EXAMPLE 7
Among a group of business leaders, believe that poor math and science education in Canada will lead to higher unemployment rates.
Convert the percent to: a) a fraction b) a decimal
a) Write ![]() |
![]() |
b) Change the fraction ![]() |
![]() |
TRY IT 7.1
Convert the percent to: a) a fraction and b) a decimal
Twitter’s share of web traffic jumped when one celebrity tweeted live on air.
Answer
TRY IT 7.2
Convert the percent to: a) a fraction and b) a decimal
Statistics Canada shows that in of adults aged
to
had a bachelor degree.
Answer
EXAMPLE 8
There are four suits of cards in a deck of cards—hearts, diamonds, clubs, and spades. The probability of randomly choosing a heart from a shuffled deck of cards is . Convert the percent to:
- a fraction
- a decimal

a) Write ![]() |
![]() |
Simplify. | ![]() |
b) Change the fraction ![]() |
![]() |
TRY IT 8.1
Convert the percent to: a) a fraction, and b) a decimal
The probability that it will rain Monday is .
Answer
TRY IT 8.2
Convert the percent to: a) a fraction, and b) a decimal
The probability of getting heads three times when tossing a coin three times is .
Answer
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 , it is easy to change that fraction to a percent.
HOW TO: Convert a Decimal to a Percent
- Write the decimal as a fraction.
- If the denominator of the fraction is not
, rewrite it as an equivalent fraction with denominator
.
- Write this ratio as a percent.
EXAMPLE 9
Convert each decimal to a percent: a) b)
a) Write ![]() |
![]() |
Write this ratio as a percent. | ![]() |
b) Write ![]() |
![]() |
Write this ratio as a percent. | ![]() |
TRY IT 9.1
Convert each decimal to a percent: a) b)
.
Answer
- 1%
- 17%
TRY IT 9.2
Convert each decimal to a percent: a) b)
Answer
- 4%
- 41%
To convert a mixed number to a percent, we first write it as an improper fraction.
EXAMPLE 10
Convert each decimal to a percent: a) b)
a) Write ![]() |
![]() |
Write as an improper fraction. The denominator is 100. | ![]() |
Write this ratio as a percent. | ![]() |
Notice that since , the result is more than
b) Write ![]() |
![]() |
Divide the numerator and denominator by 10, so that the denominator is 100. | ![]() |
Write this ratio as a percent. | ![]() |
TRY IT 10.1
Convert each decimal to a percent: a) b)
Answer
- 175%
- 8.25%
TRY IT 10.2
Convert each decimal to a percent: a) b)
Answer
- 225%
- 9.25%
Let’s summarize the results from the previous examples in the table below so we can look for a pattern.
Decimal | Percent |
---|---|
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
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.3) uses the decimal numbers in the table above and shows visually to convert them to percent by moving the decimal point two places to the right and then writing the sign.

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.
HOW TO: Convert a Fraction to a Percent
- Convert the fraction to a decimal.
- Convert the decimal to a percent.
EXAMPLE 11
Convert each fraction or mixed number to a percent: a) b)
c)
To convert a fraction to a decimal, divide the numerator by the denominator.
a) Change ![]() |
![]() |
Write as a percent by moving the decimal two places to the right. | ![]() ![]() |
b) Change ![]() |
![]() |
Write as a percent by moving the decimal two places to the right. | ![]() ![]() |
c) Write ![]() |
![]() |
Change ![]() |
![]() |
Write as a percent. | ![]() ![]() |
Notice that we needed to add zeros at the end of the number when moving the decimal two places to the right.
TRY IT 11.1
Convert each fraction or mixed number to a percent: a) b)
c)
Answer
- 62.5%
- 275%
- 340%
TRY IT 11.2
Convert each fraction or mixed number to a percent: a) b)
c)
Answer
- 87.5%
- 225%
- 160%
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.
EXAMPLE 12
Convert to a percent.
To change a fraction to a decimal, we divide the numerator by the denominator.
To convert ![]() |
![]() |
Rounding to the nearest thousandth. | ![]() |
Write as a percent. | ![]() |
TRY IT 12.1
Convert the fraction to a percent:
Answer
42.9%
TRY IT 12.2
Convert the fraction to a percent:
Answer
57.1%
When we first looked at fractions and decimals, we saw that fractions converted to a repeating decimal. When we converted the fraction to a decimal, we wrote the answer as
. We will use this same notation, as well as fraction notation, when we convert fractions to percents in the next example.
EXAMPLE 13
Statistics Canada reported in 2018 that approximately of Canadian adults are obese. Convert the fraction
to a percent.
Change ![]() ![]() ![]() |
![]() |
Write as a repeating decimal. | ![]() |
Write as a percent. | ![]() |
We could also write the percent as .
TRY IT 13.1
Convert the fraction to a percent:
According to the Canadian Census 2016, about people within the population of Canada are between the ages of
and
.
Answer
TRY IT 13.2
Convert the fraction to a percent:
According to the Canadian Census 2015, about of Canadian residents under age 18 are low income.
Answer
Key Concepts
- Convert a percent to a fraction.
- Write the percent as a ratio with the denominator 100.
- Simplify the fraction if possible.
- Convert a percent to a decimal.
- Write the percent as a ratio with the denominator 100.
- Convert the fraction to a decimal by dividing the numerator by the denominator.
- Convert a decimal to a percent.
- Write the decimal as a fraction.
- If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100.
- Write this ratio as a percent.
- Convert a fraction to a percent.
- Convert the fraction to a decimal.
- Convert the decimal to a percent.
Glossary
- percent
- A percent is a ratio whose denominator is
.
Practice Makes Perfect
Use the Definition of Percents
In the following exercises, write each percent as a ratio.
1. In ![]() ![]() |
2. In ![]() ![]() |
3. The unemployment rate for those with Bachelor’s degrees was ![]() ![]() |
4. The unemployment rate in Canada in In the following exercises, write as a) a ratio and b) a percent |
5. ![]() ![]() |
6. ![]() ![]() |
7. ![]() ![]() |
8. ![]() ![]() |
Convert Percents to Fractions and Decimals
In the following exercises, convert each percent to a fraction and simplify all fractions.
9. ![]() |
10. ![]() |
11. ![]() |
12. ![]() |
13. ![]() |
14. ![]() |
15. ![]() |
16. ![]() |
17. ![]() |
18. ![]() |
19. ![]() |
20. ![]() |
21. ![]() |
22. ![]() |
23. ![]() |
24. ![]() |
In the following exercises, convert each percent to a decimal.
25. ![]() |
26. ![]() |
27. ![]() |
28. ![]() |
29. ![]() |
30. ![]() |
31. ![]() |
32. ![]() |
33. ![]() |
34. ![]() |
35. ![]() |
36. ![]() |
37. ![]() |
38. ![]() |
39. ![]() |
40. ![]() |
In the following exercises, convert each percent to
a) a simplified fraction and
b) a decimal
41. In ![]() |
42. In ![]() |
43. According to government data, in ![]() ![]() |
44. According to the Survey of Earned Doctorates, among Canadians age ![]() ![]() |
45. A couple plans to have two children. The probability they will have two girls is ![]() |
46. Javier will choose one digit at random from ![]() ![]() ![]() ![]() |
47. According to the local weather report, the probability of thunderstorms in New York City on July ![]() ![]() |
48. A club sells ![]() ![]() |
Convert Decimals and Fractions to Percents
In the following exercises, convert each decimal to a percent.
49. ![]() |
50. ![]() |
51. ![]() |
52. ![]() |
53. ![]() |
54. ![]() |
55. ![]() |
56. ![]() |
57. ![]() |
58. ![]() |
59. ![]() |
60. ![]() |
61. ![]() |
62. ![]() |
63. ![]() |
64. ![]() |
In the following exercises, convert each fraction to a percent.
65. ![]() |
66. ![]() |
67. ![]() |
68. ![]() |
69. ![]() |
70. ![]() |
71. ![]() |
72. ![]() |
73. ![]() |
74. ![]() |
75. ![]() |
76. ![]() |
77. ![]() |
78. ![]() |
79. ![]() |
80. ![]() |
In the following exercises, convert each fraction to a percent.
81. ![]() |
82. ![]() |
In the following exercises, convert each fraction to a percent.
83. According to the Government of Canada, in ![]() |
84. Statistics Canada showed that in ![]() |
In the following exercises, complete the table.
85.
|
86.
|
Writing Exercises
87. Convert ![]() |
88. Convert ![]() ![]() |
89. When the Szetos sold their home, the selling price was ![]() ![]() ![]() |
90. According to cnn.com, cell phone use in ![]() ![]() ![]() ![]() |
Answers
1. ![]() |
3. ![]() |
5.
a) b) |
7.
a) b) |
9. ![]() |
11. ![]() |
13. ![]() |
15. ![]() |
17. ![]() |
19. ![]() |
21. ![]() |
23. ![]() |
25. 0.05 | 27. 0.01 | 29. 0.63 |
31. 0.4 | 33. 1.15 | 35. 1.5 |
37. 0.214 | 39. 0.078 | 41.
a) b) |
43.
a) b) |
45.
a) b) |
47.
a) b) |
49. 1% | 51. 18% | 53. 135% |
55. 300% | 57. 0.9% | 59. 8.75% |
61. 150% | 63. 225.4% | 65. 25% |
67. 37.5% | 69. 175% | 71. 680% |
73. 41.7% | 75. ![]() |
77. 42.9% |
79. 55.6% | 81. 25% | 83. 64% |
87. ![]() |
89. The Szetos sold their home for five times what they paid 30 years ago. |
Attributions
This chapter has been adapted from “Understand Percent” in Prealgebra (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.