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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.

6 is in the tenths position of 0.6

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

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

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3 is in the thousandths position of 0.903

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

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1 is in the hundredths position of 18.61

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

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5 is in the ten thousandths position of 508.0005

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

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

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Practice set a

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

16.84

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

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0.513

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

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6,646.0107

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

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1.1

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

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Converting a complex decimal to a fraction

Complex decimals

Numbers such as 0 . 11 2 3 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.

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

The 2 3 size 12{ { {2} over {3} } } {} appears to occur in the thousands position, but it is referring to 2 3 size 12{ { {2} over {3} } } {} of a hundredth. So, we read 0 . 11 2 3 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

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

Note that 4 . 006 1 4 = 4 + . 006 1 4 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

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Practice set b

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

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

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

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

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

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

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

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

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

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Exercises

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

0.7

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

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0.53

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

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0.219

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

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4.8

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

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16.12

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

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6.0005

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

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16.125

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

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3.04

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

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8.225

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

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9.99995

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Exercises for review

( [link] ) Find the greatest common factor of 70, 182, and 154.

14

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( [link] ) Find the greatest common multiple of 14, 26, and 60.

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( [link] ) Find the value of 3 5 15 18 ÷ 5 9 size 12{ { {3} over {5} } cdot { {"15"} over {"18"} } div { {5} over {9} } } {} .

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

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( [link] ) Find the value of 5 2 3 + 8 1 12 size 12{5 { {2} over {3} } +8 { {1} over {"12"} } } {} .

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( [link] ) In the decimal number 26.10742, the digit 7 is in what position?

thousandths

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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