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Converting a Decimal to a Fraction

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 covert a decimal to a fraction. By the end of the module students should be able to convert an ordinary decimal and a complex decimal to a fraction.

Section Overview

  • Converting an Ordinary Decimal to a Fraction
  • Converting a Complex Decimal to a Fraction

Converting an Ordinary Decimal to a Fraction

We can convert a decimal fraction to a fraction, essentially, by saying it in words, then writing what we say. We may have to reduce that fraction.

Sample Set A

Convert each decimal fraction to a proper fraction or a mixed number.

Example 1

6 is in the tenths position of 0.6

Reading: six tenths→ 610610 size 12{ { {6} over {10} } } {}.

Reduce: 3535 size 12{ { {3} over {5} } } {}.

Example 2

3 is in the thousandths position of 0.903

Reading: nine hundred three thousands→ 90310009031000 size 12{ { {"903"} over {"1000"} } } {}.

Example 3

1 is in the hundredths position of 18.61

Reading: eighteen and sixty-one hundredths→ 18611001861100 size 12{"18" { {"61"} over {"100"} } } {}.

Example 4

5 is in the ten thousandths position of 508.0005

Reading: five hundred eight and five ten thousandths→ 508510,000508510,000 size 12{"508" { {5} over {"10","000"} } } {}.

Reduce: 50812,00050812,000 size 12{"508" { {1} over {2,"000"} } } {}.

Practice Set A

Convert the following decimals to fractions or mixed numbers. Be sure to reduce.

Exercise 1

16.84

Solution

162125162125 size 12{"16" { {"21"} over {"25"} } } {}

Exercise 2

0.513

Solution

5131,0005131,000 size 12{ { {"513"} over {1,"000"} } } {}

Exercise 3

6,646.0107

Solution

6,64610710,0006,64610710,000 size 12{6,"646" { {"107"} over {"10","000"} } } {}

Exercise 4

1.1

Solution

11101110 size 12{1 { {1} over {"10"} } } {}

Converting A Complex Decimal to a Fraction

Complex Decimals

Numbers such as 0.11230.1123 size 12{0 "." "11" { {2} over {3} } } {} are called complex decimals. We can also convert com­plex decimals to fractions.

Sample Set B

Convert the following complex decimals to fractions.

Example 5

0.11230.1123 size 12{0 "." "11" { {2} over {3} } } {}

The 2323 size 12{ { {2} over {3} } } {} appears to occur in the thousands position, but it is referring to 2323 size 12{ { {2} over {3} } } {} of a hundredth. So, we read 0.11230.1123 size 12{0 "." "11" { {2} over {3} } } {} as "eleven and two-thirds hundredths."

0.11 2 3 = 11 2 3 100 = 11 ⋅ 3 + 2 3 100 = 35 3 100 1 = 35 3 ÷ 100 1 = 35 7 3 ⋅ 1 100 20 = 7 60 0.11 2 3 = 11 2 3 100 = 11 ⋅ 3 + 2 3 100 = 35 3 100 1 = 35 3 ÷ 100 1 = 35 7 3 ⋅ 1 100 20 = 7 60

Example 6

4.006144.00614 size 12{4 "." "006" { {1} over {4} } } {}

Note that 4.00614=4+.006144.00614=4+.00614 size 12{4 "." "006" { {1} over {4} } =4+ "." "006" { {1} over {4} } } {}

4 + .006 1 4 = 4 + 6 1 4 1000 = 4 + 25 4 1000 1 = 4 + 25 1 4 ⋅ 1 1000 40 = 4 + 1 ⋅ 1 4 ⋅ 40 = 4 + 1 160 = 4 1 160 4 + .006 1 4 = 4 + 6 1 4 1000 = 4 + 25 4 1000 1 = 4 + 25 1 4 ⋅ 1 1000 40 = 4 + 1 ⋅ 1 4 ⋅ 40 = 4 + 1 160 = 4 1 160

Practice Set B

Convert each complex decimal to a fraction or mixed number. Be sure to reduce.

Exercise 5

0.8340.834 size 12{0 "." 8 { {3} over {4} } } {}

Solution

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

Exercise 6

0.12250.1225 size 12{0 "." "12" { {2} over {5} } } {}

Solution

3125031250 size 12{ { {"31"} over {"250"} } } {}

Exercise 7

6.005566.00556 size 12{6 "." "005" { {5} over {6} } } {}

Solution

671,200671,200 size 12{6 { {7} over {1,"200"} } } {}

Exercise 8

18.131718.1317 size 12{"18" "." 1 { {3} over {"17"} } } {}

Solution

1821718217 size 12{"18" { {2} over {"17"} } } {}

Exercises

For the following 20 problems, convert each decimal fraction to a proper fraction or a mixed number. Be sure to reduce.

Exercise 9

0.7

Solution

710710 size 12{ { {7} over {"10"} } } {}

Exercise 10

0.1

Exercise 11

0.53

Solution

5310053100 size 12{ { {"53"} over {"100"} } } {}

Exercise 12

0.71

Exercise 13

0.219

Solution

2191,0002191,000 size 12{ { {"219"} over {1,"000"} } } {}

Exercise 14

0.811

Exercise 15

4.8

Solution

445445 size 12{4 { {4} over {5} } } {}

Exercise 16

2.6

Exercise 17

16.12

Solution

1632516325 size 12{"16" { {3} over {"25"} } } {}

Exercise 18

25.88

Exercise 19

6.0005

Solution

612,000612,000 size 12{6 { {1} over {2,"000"} } } {}

Exercise 20

1.355

Exercise 21

16.125

Solution

16181618 size 12{"16" { {1} over {8} } } {}

Exercise 22

0.375

Exercise 23

3.04

Solution

31253125 size 12{3 { {1} over {"25"} } } {}

Exercise 24

21.1875

Exercise 25

8.225

Solution

89408940 size 12{8 { {9} over {"40"} } } {}

Exercise 26

1.0055

Exercise 27

9.99995

Solution

919,99920,000919,99920,000 size 12{9 { {"19","999"} over {"20","000"} } } {}

Exercise 28

22.110

For the following 10 problems, convert each complex decimal to a fraction.

Exercise 29

0.7120.712 size 12{0 "." 7 { {1} over {2} } } {}

Solution

3434 size 12{ { {3} over {4} } } {}

Exercise 30

0.012120.01212 size 12{0 "." "012" { {1} over {2} } } {}

Exercise 31

2.16142.1614 size 12{2 "." "16" { {1} over {4} } } {}

Solution

2138021380 size 12{2 { {"13"} over {"80"} } } {}

Exercise 32

5.18235.1823 size 12{5 "." "18" { {2} over {3} } } {}

Exercise 33

14.1121314.11213 size 12{"14" "." "112" { {1} over {3} } } {}

Solution

143373,000143373,000 size 12{"14" { {"337"} over {3,"000"} } } {}

Exercise 34

80.00113780.001137 size 12{"80" "." "0011" { {3} over {7} } } {}

Exercise 35

1.405161.40516 size 12{1 "." "40" { {5} over {"16"} } } {}

Solution

11293201129320 size 12{1 { {"129"} over {"320"} } } {}

Exercise 36

0.8530.853 size 12{0 "." 8 { {5} over {3} } } {}

Exercise 37

1.9751.975 size 12{1 "." 9 { {7} over {5} } } {}

Solution

21252125 size 12{2 { {1} over {"25"} } } {}

Exercise 38

1.73791.7379 size 12{1 "." 7 { {"37"} over {9} } } {}

Exercises for Review

Exercise 39

((Reference)) Find the greatest common factor of 70, 182, and 154.

Solution

14

Exercise 40

((Reference)) Find the greatest common multiple of 14, 26, and 60.

Exercise 41

((Reference)) Find the value of 35⋅1518÷5935⋅1518÷59 size 12{ { {3} over {5} } cdot { {"15"} over {"18"} } div { {5} over {9} } } {}.

Solution

910910 size 12{ { {9} over {"10"} } } {}

Exercise 42

((Reference)) Find the value of 523+8112523+8112 size 12{5 { {2} over {3} } +8 { {1} over {"12"} } } {}.

Exercise 43

((Reference)) In the decimal number 26.10742, the digit 7 is in what position?

Solution

thousandths

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