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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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Questions & Answers

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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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LITNING Reply
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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Bob
The nanotechnology is as new science, to scale nanometric
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nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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Adin Reply
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
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s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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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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