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Decimals: Converting a Fraction to a Decimal

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to convert a fraction to a decimal. By the end of the module students should be able to convert a fraction to a decimal.

Now that we have studied and practiced dividing with decimals, we are also able to convert a fraction to a decimal. To do so we need only recall that a fraction bar can also be a division symbol. Thus, 3434 size 12{ { {3} over {4} } } {} not only means "3 objects out of 4," but can also mean "3 divided by 4."

Sample Set A

Convert the following fractions to decimals. If the division is nonterminating, round to two decimal places.

Example 1

3434 size 12{ { {3} over {4} } } {}. Divide 3 by 4.

.75 4 3.00 2 8   ̲ 20 20 ̲ 0 .75 4 3.00 2 8   ̲ 20 20 ̲ 0

Thus, 34=0.7534=0.75 size 12{ { {3} over {4} } =0 "." "75"} {}.

Example 2

1515 size 12{ { {1} over {5} } } {} Divide 1 by 5.

.2 5 1.0 1.0 ̲ 0 .2 5 1.0 1.0 ̲ 0

Thus, 15=0.215=0.2 size 12{ { {1} over {5} } =0 "." 2} {}

Example 3

5656 size 12{ { {5} over {6} } } {}. Divide 5 by 6.

Long division. 5 divided by 6 ends in a recurring remainder. The quotient is .833. The recurring remainder indicates that the division is nonterminating.

56=0.833⋯56=0.833⋯ size 12{ { {5} over {6} } =0 "." "833" dotsaxis } {} We are to round to two decimal places.

Thus, 56=0.8356=0.83 size 12{ { {5} over {6} } =0 "." "83"} {} to two decimal places.

Example 4

518518 size 12{5 { {1} over {8} } } {}. Note that 518=5+18518=5+18 size 12{5 { {1} over {8} } =5+ { {1} over {8} } } {}.

Convert 1818 size 12{ { {1} over {8} } } {} to a decimal.

.125 8 1.000   8     ̲ 20   16   ̲ 40 40 ̲ 0 .125 8 1.000   8     ̲ 20   16   ̲ 40 40 ̲ 0

1 8 = . 125 1 8 = . 125 size 12{ { {1} over {8} } = "." "125"} {}

Thus, 518=5+18=5+.125=5.125518=5+18=5+.125=5.125 size 12{5 { {1} over {8} } =5+ { {1} over {8} } =5+ "." "125"=5 "." "125"} {}.

Example 5

0.16140.1614 size 12{0 "." "16" { {1} over {4} } } {} . This is a complex decimal.

Note that the 6 is in the hundredths position.

The number 0.16140.1614 size 12{0 "." "16" { {1} over {4} } } {} is read as "sixteen and one-fourth hundredths."

0 . 16 1 4 = 16 1 4 100 = 16 ⋅ 4 + 1 4 100 = 65 4 100 1 = 65 13 4 ⋅ 1 100 20 = 13 ⋅ 1 4 ⋅ 20 = 13 80 0 . 16 1 4 = 16 1 4 100 = 16 ⋅ 4 + 1 4 100 = 65 4 100 1 = 65 13 4 ⋅ 1 100 20 = 13 ⋅ 1 4 ⋅ 20 = 13 80 size 12{0 "." "16" { {1} over {4} } = { {"16" { {1} over {4} } } over {"100"} } = { { { {"16" cdot 4+1} over {4} } } over {"100"} } = { { { {"65"} over {4} } } over { { {"100"} over {1} } } } = { { {"65"} cSup { size 8{"13"} } } over {4} } cdot { {1} over { {"100"} cSub { size 8{"20"} } } } = { {"13" cdot 1} over {4 cdot "20"} } = { {"13"} over {"80"} } } {}

Now, convert 13801380 size 12{ { {"13"} over {"80"} } } {} to a decimal.

.1625 80 13.0000 8 0       ̲ 5 00     4 80     ̲ 200   160   ̲ 400 400 ̲ 0 .1625 80 13.0000 8 0       ̲ 5 00     4 80     ̲ 200   160   ̲ 400 400 ̲ 0

Thus, 0.1614=0.16250.1614=0.1625 size 12{0 "." "16" { {1} over {4} } =0 "." "1625"} {}.

Practice Set A

Convert the following fractions and complex decimals to decimals (in which no proper fractions appear). If the divison is nonterminating, round to two decimal places.

Exercise 1

1414 size 12{ { {1} over {4} } } {}

Solution

0.25

Exercise 2

125125 size 12{ { {1} over {"25"} } } {}

Solution

0.04

Exercise 3

1616 size 12{ { {1} over {6} } } {}

Solution

0.17

Exercise 4

15161516 size 12{ { {"15"} over {"16"} } } {}

Solution

0.9375

Exercise 5

0.9120.912 size 12{0 "." 9 { {1} over {2} } } {}

Solution

0.95

Exercise 6

8.0126388.012638 size 12{8 "." "0126" { {3} over {8} } } {}

Solution

8.0126375

Exercises

For the following 30 problems, convert each fraction or complex decimal number to a decimal (in which no proper fractions appear).

Exercise 7

1212 size 12{ { {1} over {2} } } {}

Solution

0.5

Exercise 8

4545 size 12{ { {4} over {5} } } {}

Exercise 9

7878 size 12{ { {7} over {8} } } {}

Solution

0.875

Exercise 10

5858 size 12{ { {5} over {8} } } {}

Exercise 11

3535 size 12{ { {3} over {5} } } {}

Solution

0.6

Exercise 12

2525 size 12{ { {2} over {5} } } {}

Exercise 13

125125 size 12{ { {1} over {"25"} } } {}

Solution

0.04

Exercise 14

325325 size 12{ { {3} over {"25"} } } {}

Exercise 15

120120 size 12{ { {1} over {"20"} } } {}

Solution

0.05

Exercise 16

115115 size 12{ { {1} over {"15"} } } {}

Exercise 17

150150 size 12{ { {1} over {"50"} } } {}

Solution

0.02

Exercise 18

175175 size 12{ { {1} over {"75"} } } {}

Exercise 19

1313 size 12{ { {1} over {3} } } {}

Solution

0.3¯0.3¯ size 12{0 "." {overline {3}} } {}

Exercise 20

5656 size 12{ { {5} over {6} } } {}

Exercise 21

316316 size 12{ { {3} over {"16"} } } {}

Solution

0.1875

Exercise 22

916916 size 12{ { {9} over {"16"} } } {}

Exercise 23

127127 size 12{ { {1} over {"27"} } } {}

Solution

0.037¯0.037¯ size 12{0 "." 0 {overline {"37"}} } {}

Exercise 24

527527 size 12{ { {5} over {"27"} } } {}

Exercise 25

713713 size 12{ { {7} over {"13"} } } {}

Solution

0.538461¯0.538461¯ size 12{0 "." {overline {"538461"}} } {}

Exercise 26

914914 size 12{ { {9} over {"14"} } } {}

Exercise 27

723723 size 12{7 { {2} over {3} } } {}

Solution

7.6¯7.6¯ size 12{7 "." {overline {6}} } {}

Exercise 28

85168516 size 12{8 { {5} over {"16"} } } {}

Exercise 29

12151215 size 12{1 { {2} over {"15"} } } {}

Solution

1.13¯1.13¯ size 12{1 "." 1 {overline {3}} } {}

Exercise 30

6552265522 size 12{"65" { {5} over {"22"} } } {}

Exercise 31

101625101625 size 12{"101" { {6} over {"25"} } } {}

Solution

101.24

Exercise 32

0.1120.112 size 12{0 "." 1 { {1} over {2} } } {}

Exercise 33

0.24180.2418 size 12{0 "." "24" { {1} over {8} } } {}

Solution

0.24125

Exercise 34

5.66235.6623 size 12{5 "." "66" { {2} over {3} } } {}

Exercise 35

810.3106516810.3106516 size 12{"810" "." "3106" { {5} over {"16"} } } {}

Solution

810.31063125

Exercise 36

4.1194.119 size 12{4 "." 1 { {1} over {9} } } {}

For the following 18 problems, convert each fraction to a decimal. Round to five decimal places.

Exercise 37

1919 size 12{ { {1} over {9} } } {}

Solution

0.11111

Exercise 38

2929 size 12{ { {2} over {9} } } {}

Exercise 39

3939 size 12{ { {3} over {9} } } {}

Solution

0.33333

Exercise 40

4949 size 12{ { {4} over {9} } } {}

Exercise 41

5959 size 12{ { {5} over {9} } } {}

Solution

0.55556

Exercise 42

6969 size 12{ { {6} over {9} } } {}

Exercise 43

7979 size 12{ { {7} over {9} } } {}

Solution

0.77778

Exercise 44

8989 size 12{ { {8} over {9} } } {}

Exercise 45

111111 size 12{ { {1} over {"11"} } } {}

Solution

0.09091

Exercise 46

211211 size 12{ { {2} over {"11"} } } {}

Exercise 47

311311 size 12{ { {3} over {"11"} } } {}

Solution

0.27273

Exercise 48

411411 size 12{ { {4} over {"11"} } } {}

Exercise 49

511511 size 12{ { {5} over {"11"} } } {}

Solution

0.45455

Exercise 50

611611 size 12{ { {6} over {"11"} } } {}

Exercise 51

711711 size 12{ { {7} over {"11"} } } {}

Solution

0.63636

Exercise 52

811811 size 12{ { {8} over {"11"} } } {}

Exercise 53

911911 size 12{ { {9} over {"11"} } } {}

Solution

0.81818

Exercise 54

10111011 size 12{ { {"10"} over {"11"} } } {}

Calculator Problems

For the following problems, use a calculator to convert each fraction to a decimal. If no repeating pattern seems to exist, round to four decimal places.

Exercise 55

1612516125 size 12{ { {"16"} over {"125"} } } {}

Solution

0.128

Exercise 56

8531185311 size 12{ { {"85"} over {"311"} } } {}

Exercise 57

192197192197 size 12{ { {"192"} over {"197"} } } {}

Solution

0.9746

Exercise 58

1146911469 size 12{ { {1} over {"1469"} } } {}

Exercise 59

421,015421,015 size 12{ { {4} over {"21","015"} } } {}

Solution

0.0002

Exercise 60

81,426106,00181,426106,001 size 12{ { {"81","426"} over {"106","001"} } } {}

Exercise 61

16,50142616,501426 size 12{ { {"16","501"} over {"426"} } } {}

Solution

38.7347

Exercises for Review

Exercise 62

((Reference)) Round 2,105,106 to the nearest hundred thousand.

Exercise 63

((Reference)) 8585 size 12{ { {8} over {5} } } {} of what number is 3232 size 12{ { {3} over {2} } } {}?

Solution

15161516 size 12{ { {"15"} over {"16"} } } {}

Exercise 64

((Reference)) Arrange 19161916 size 12{1 { {9} over {"16"} } } {}, 158158 size 12{1 { {5} over {8} } } {}, and 17121712 size 12{1 { {7} over {"12"} } } {} in increasing order.

Exercise 65

((Reference)) Convert the complex decimal 3.6543.654 size 12{3 "." 6 { {5} over {4} } } {} to a fraction.

Solution

3294032940 size 12{3 { {"29"} over {"40"} } } {} or 3.725

Exercise 66

((Reference)) Find the quotient. 30÷1.130÷1.1 size 12{"30" div 1 "." 1} {}.

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