# 6.2 Converting a decimal to a fraction

 Page 1 / 1
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. Reading: six tenths→ $\frac{6}{10}$ .

Reduce: $\frac{3}{5}$ . Reading: nine hundred three thousands→ $\frac{\text{903}}{\text{1000}}$ . Reading: eighteen and sixty-one hundredths→ $\text{18}\frac{\text{61}}{\text{100}}$ . Reading: five hundred eight and five ten thousandths→ $\text{508}\frac{5}{\text{10},\text{000}}$ .

Reduce: $\text{508}\frac{1}{2,\text{000}}$ .

## Practice set a

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

16.84

$\text{16}\frac{\text{21}}{\text{25}}$

0.513

$\frac{\text{513}}{1,\text{000}}$

6,646.0107

$6,\text{646}\frac{\text{107}}{\text{10},\text{000}}$

1.1

$1\frac{1}{\text{10}}$

## Complex decimals

Numbers such as $0\text{.}\text{11}\frac{2}{3}$ are called complex decimals . We can also convert com­plex decimals to fractions.

## Sample set b

Convert the following complex decimals to fractions.

$0\text{.}\text{11}\frac{2}{3}$

The $\frac{2}{3}$ appears to occur in the thousands position, but it is referring to $\frac{2}{3}$ of a hundredth. So, we read $0\text{.}\text{11}\frac{2}{3}$ as "eleven and two-thirds hundredths."

$\begin{array}{ccc}0.11\frac{2}{3}=\frac{\text{11}\frac{2}{3}}{\text{100}}& =& \frac{\frac{\text{11}\cdot 3+2}{3}}{\text{100}}\\ & =& \frac{\frac{\text{35}}{3}}{\frac{\text{100}}{1}}\hfill \\ & =& \frac{\text{35}}{3}÷\frac{\text{100}}{1}\hfill \\ & =& \frac{\stackrel{7}{\overline{)35}}}{3}\cdot \frac{1}{\underset{\text{20}}{\overline{)100}}}\hfill \\ & =& \frac{7}{\text{60}}\hfill \end{array}$

$4\text{.}\text{006}\frac{1}{4}$

Note that $4\text{.}\text{006}\frac{1}{4}=4+\text{.}\text{006}\frac{1}{4}$

$\begin{array}{ccc}\hfill 4+.006\frac{1}{4}& =& 4+\frac{6\frac{1}{4}}{\text{1000}}\hfill \\ & =& 4+\frac{\frac{\text{25}}{4}}{\frac{\text{1000}}{1}}\hfill \\ & =& 4+\frac{\stackrel{1}{\overline{)25}}}{4}\cdot \frac{1}{\underset{40}{\overline{)1000}}}\hfill \\ & =& 4+\frac{1\cdot 1}{4\cdot \text{40}}\hfill \\ & =& 4+\frac{1}{\text{160}}\hfill \\ & =& 4\frac{1}{\text{160}}\hfill \end{array}$

## Practice set b

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

$0\text{.}8\frac{3}{4}$

$\frac{7}{8}$

$0\text{.}\text{12}\frac{2}{5}$

$\frac{\text{31}}{\text{250}}$

$6\text{.}\text{005}\frac{5}{6}$

$6\frac{7}{1,\text{200}}$

$\text{18}\text{.}1\frac{3}{\text{17}}$

$\text{18}\frac{2}{\text{17}}$

## Exercises

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

0.7

$\frac{7}{\text{10}}$

0.1

0.53

$\frac{\text{53}}{\text{100}}$

0.71

0.219

$\frac{\text{219}}{1,\text{000}}$

0.811

4.8

$4\frac{4}{5}$

2.6

16.12

$\text{16}\frac{3}{\text{25}}$

25.88

6.0005

$6\frac{1}{2,\text{000}}$

1.355

16.125

$\text{16}\frac{1}{8}$

0.375

3.04

$3\frac{1}{\text{25}}$

21.1875

8.225

$8\frac{9}{\text{40}}$

1.0055

9.99995

$9\frac{\text{19},\text{999}}{\text{20},\text{000}}$

22.110

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

$0\text{.}7\frac{1}{2}$

$\frac{3}{4}$

$0\text{.}\text{012}\frac{1}{2}$

$2\text{.}\text{16}\frac{1}{4}$

$2\frac{\text{13}}{\text{80}}$

$5\text{.}\text{18}\frac{2}{3}$

$\text{14}\text{.}\text{112}\frac{1}{3}$

$\text{14}\frac{\text{337}}{3,\text{000}}$

$\text{80}\text{.}\text{0011}\frac{3}{7}$

$1\text{.}\text{40}\frac{5}{\text{16}}$

$1\frac{\text{129}}{\text{320}}$

$0\text{.}8\frac{5}{3}$

$1\text{.}9\frac{7}{5}$

$2\frac{1}{\text{25}}$

$1\text{.}7\frac{\text{37}}{9}$

## Exercises for review

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

14

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

( [link] ) Find the value of $\frac{3}{5}\cdot \frac{\text{15}}{\text{18}}÷\frac{5}{9}$ .

$\frac{9}{\text{10}}$

( [link] ) Find the value of $5\frac{2}{3}+8\frac{1}{\text{12}}$ .

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

thousandths

#### Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min
Tanis Reply

### Read also:

#### 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? By   By By  By By Mldelatte  By