<< Chapter < Page Chapter >> Page >
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} } } {} .

Got questions? Get instant answers now!

3 is in the thousandths position of 0.903

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

Got questions? Get instant answers now!

1 is in the hundredths position of 18.61

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

Got questions? Get instant answers now!

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"} } } {} .

Got questions? Get instant answers now!

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"} } } {}

Got questions? Get instant answers now!

0.513

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

Got questions? Get instant answers now!

6,646.0107

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

Got questions? Get instant answers now!

1.1

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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} } } {}

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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"} } } {}

Got questions? Get instant answers now!

0.53

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

Got questions? Get instant answers now!

0.219

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

Got questions? Get instant answers now!

4.8

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

Got questions? Get instant answers now!

16.12

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

Got questions? Get instant answers now!

6.0005

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

Got questions? Get instant answers now!

16.125

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

Got questions? Get instant answers now!

3.04

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

Got questions? Get instant answers now!

8.225

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

Got questions? Get instant answers now!

9.99995

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

Got questions? Get instant answers now!

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} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Exercises for review

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

14

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( [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"} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

thousandths

Got questions? Get instant answers now!

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
7hours 36 min - 4hours 50 min
Tanis Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask