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Arithmetic Review: Percent

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

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Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Overview

  • The Meaning of Percent
  • Converting A Fraction To A Percent
  • Converting A Decimal To A Percent
  • Converting A Percent To A Decimal

The Meaning of Percent

The word percent comes from the Latin word “per centum,” “per” meaning “for each,” and “centum” meaning “hundred.”

Percent (%)

Percent means “for each hundred” or “for every hundred.” The symbol % is used to represent the word percent.

Thus, 1%= 1 100 or 1%=0.01. 1%= 1 100 or 1%=0.01.

Converting A Fraction To A Percent

We can see how a fraction can be converted to a percent by analyzing the method that 3 5 3 5 is converted to a percent. In order to convert 3 5 3 5 to a percent, we need to introduce 1 100 1 100 (since percent means for each hundred).

Example 1

3 5 = 3 5  ·  100 100 Multiply the fraction by 1. = 3 5  · 100 ·  1 100 Since   100 100 =100 ·  1 100 . = 300 5  ·  1 100 Divide 300 by 5. = 60 ·  1 100 Multiply the fractions. = 60% Replace  1 100  with the % symbol. 3 5 = 3 5  ·  100 100 Multiply the fraction by 1. = 3 5  · 100 ·  1 100 Since   100 100 =100 ·  1 100 . = 300 5  ·  1 100 Divide 300 by 5. = 60 ·  1 100 Multiply the fractions. = 60% Replace  1 100  with the % symbol.

Fraction to Percent

To convert a fraction to a percent, multiply the fraction by 1 in the form 100 ·  1 100 100 ·  1 100 , then replace 1 100 1 100 with the % symbol.

Sample Set A

Convert each fraction to a percent.

Example 2

1 4 = 1 4  · 100 ·  1 100 = 100 4  ·  1 100 = 25 ·  1 100 = 25% 1 4 = 1 4  · 100 ·  1 100 = 100 4  ·  1 100 = 25 ·  1 100 = 25%

Example 3

8 5 = 8 5  · 100 ·  1 100 = 800 5  ·  1 100 = 160% 8 5 = 8 5  · 100 ·  1 100 = 800 5  ·  1 100 = 160%

Example 4

4 9 = 4 9  · 100 ·  1 100 = 400 9  ·  1 100 = ( 44.4... ) ·  1 100 = ( 44. 4 ¯ ) ·  1 100 = 44. 4 ¯ % 4 9 = 4 9  · 100 ·  1 100 = 400 9  ·  1 100 = ( 44.4... ) ·  1 100 = ( 44. 4 ¯ ) ·  1 100 = 44. 4 ¯ %

Converting A Decimal To A Percent

We can see how a decimal is converted to a percent by analyzing the method that 0.75 0.75 is converted to a percent. We need to introduce 1 100 . 1 100 .

0.75 = 0.75 · 100 ·  1 100 Multiply the decimal by 1. = 75 ·  1 100 = 75% Replace  1 100  with the % symbol. 0.75 = 0.75 · 100 ·  1 100 Multiply the decimal by 1. = 75 ·  1 100 = 75% Replace  1 100  with the % symbol.

Decimal to Percent

To convert a fraction to a percent, multiply the decimal by 1 in the form 100 ·  1 100 100 ·  1 100 , then replace 1 100 1 100 with the % symbol. This amounts to moving the decimal point 2 places to the right.

Sample Set B

Convert each decimal to a percent.

Example 5

0.62 = 0.62 · 100 ·  1 100 = 62 ·  1 100 = 62% 0.62 = 0.62 · 100 ·  1 100 = 62 ·  1 100 = 62%

Notice that the decimal point in the original number has been moved to the right 2 places.

Example 6

8.4 = 8.4 · 100 ·  1 100 = 840 ·  1 100 = 840% 8.4 = 8.4 · 100 ·  1 100 = 840 ·  1 100 = 840%

Notice that the decimal point in the original number has been moved to the right 2 places.

Example 7

0.47623 = 0.47623 · 100 ·  1 100 = 0.47623 ·  1 100 = 47.623% 0.47623 = 0.47623 · 100 ·  1 100 = 0.47623 ·  1 100 = 47.623%

Notice that the decimal point in the original number has been moved to the right 2 places.

Converting A Percent To A Decimal

We can see how a percent is converted to a decimal by analyzing the method that 12% is converted to a decimal. We need to introduce 1 100 . 1 100 .

12% = 12 ·  1 100 Replace % with  1 100 . = 12 100 Multiply the fractions. = 0.12 Divide 12 by 100. 12% = 12 ·  1 100 Replace % with  1 100 . = 12 100 Multiply the fractions. = 0.12 Divide 12 by 100.

Percent to Decimal

To convert a percent to a decimal, replace the % symbol with 1 100 , 1 100 , then divide the number by 100. This amounts to moving the decimal point 2 places to the left.

Sample Set C

Convert each percent to a decimal.

Example 8

48% = 48 ·  1 100 = 48 100 = 0.48 48% = 48 ·  1 100 = 48 100 = 0.48

Notice that the decimal point in the original number has been moved to the left 2 places.

Example 9

659% = 659 ·  1 100 = 659 100 = 6.59 659% = 659 ·  1 100 = 659 100 = 6.59

Notice that the decimal point in the original number has been moved to the left 2 places.

Example 10

0.4113% = 0.4113 ·  1 100 = 0.4113 100 = 0.004113 0.4113% = 0.4113 ·  1 100 = 0.4113 100 = 0.004113

Notice that the decimal point in the original number has been moved to the left 2 places.

Exercises

For the following problems, convert each fraction to a percent.

Exercise 1

2 5 2 5

Solution

40% 40%

Exercise 2

7 8 7 8

Exercise 3

1 8 1 8

Solution

12.5% 12.5%

Exercise 4

5 16 5 16

Exercise 5

15÷22 15÷22

Solution

68.18% 68.18%

Exercise 6

2 11 2 11

Exercise 7

2 9 2 9

Solution

22.22% 22.22%

Exercise 8

16 45 16 45

Exercise 9

27 55 27 55

Solution

49.09% 49.09%

Exercise 10

7 27 7 27

Exercise 11

15

Solution

1500% 1500%

Exercise 12

8

For the following problems, convert each decimal to a percent.

Exercise 13

0.36 0.36

Solution

36% 36%

Exercise 14

0.42 0.42

Exercise 15

0.446 0.446

Solution

44.6% 44.6%

Exercise 16

0.1298 0.1298

Exercise 17

4.25 4.25

Solution

425% 425%

Exercise 18

5.875 5.875

Exercise 19

86.98 86.98

Solution

8698% 8698%

Exercise 20

21.26 21.26

Exercise 21

14

Solution

1400% 1400%

Exercise 22

12

For the following problems, convert each percent to a decimal.

Exercise 23

35% 35%

Solution

0.35 0.35

Exercise 24

76% 76%

Exercise 25

18.6% 18.6%

Solution

0.186 0.186

Exercise 26

67.2% 67.2%

Exercise 27

9.0145% 9.0145%

Solution

0.090145 0.090145

Exercise 28

3.00156% 3.00156%

Exercise 29

0.00005% 0.00005%

Solution

0.0000005 0.0000005

Exercise 30

0.00034% 0.00034%

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