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Arithmetic Review: Percent

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

Summary: This module contains the an arithmetic review from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

Note: You are viewing an old version of this document. The latest version is available here.

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

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

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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