OpenStax-CNX module: m34958
1
Decimals: Converting a Decimal to
∗
a Fraction
Wade Ellis
Denny Burzynski
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0
†
Abstract
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr.
module discusses how to covert a decimal to a fraction.
This
By the end of the module students should be
able to convert an ordinary decimal and a complex decimal to a fraction.
1 Section Overview
• Converting an Ordinary Decimal to a Fraction
• Converting a Complex Decimal to a Fraction
2 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.
2.1 Sample Set A
Convert each decimal fraction to a proper fraction or a mixed number.
Example 1
Reading: six tenths→
Reduce: 35 .
6
10 .
Example 2
Reading: nine hundred three thousands→
∗ Version
1.2: Aug 18, 2010 8:18 pm -0500
† http://creativecommons.org/licenses/by/3.0/
http://cnx.org/content/m34958/1.2/
903
1000
.
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2
Example 3
61
.
Reading: eighteen and sixty-one hundredths→ 18 100
Example 4
Reading: ve hundred eight and ve ten thousandths→ 508 10,5000 .
1
Reduce: 508 2,000
.
2.2 Practice Set A
Convert the following decimals to fractions or mixed numbers. Be sure to reduce.
Exercise 1
(Solution on p. 6.)
Exercise 2
(Solution on p. 6.)
Exercise 3
(Solution on p. 6.)
Exercise 4
(Solution on p. 6.)
16.84
0.513
6,646.0107
1.1
3 Converting A Complex Decimal to a Fraction
Complex Decimals
Numbers such as 0.11 23 are called complex decimals. We can also convert complex decimals to fractions.
3.1 Sample Set B
Convert the following complex decimals to fractions.
Example 5
0.11 23
The 32 appears to occur in the thousands position, but it is referring to
we read 0.11 23 as "eleven and two-thirds hundredths."
0.11 32 =
2
11 3
100
11·3+2
=
3
100
35
3
100
=
1
=
35
3
÷
100
·
1
)100
20
1
7
=
)35
3
=
http://cnx.org/content/m34958/1.2/
7
60
2
3
of a hundredth. So,
OpenStax-CNX module: m34958
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Example 6
4.006 14
Note that 4.006 14 = 4 + .006 14
4 + .006 14
=
4+
=
4+
6 14
1000
25
4
1000
1
1
=
4+
)25
4
·
1
)1000
40
=
4+
=
4+
=
1·1
4·40
1
160
1
4 160
3.2 Practice Set B
Convert each complex decimal to a fraction or mixed number. Be sure to reduce.
Exercise 5
(Solution on p. 6.)
Exercise 6
(Solution on p. 6.)
Exercise 7
(Solution on p. 6.)
Exercise 8
(Solution on p. 6.)
0.8 34
0.12 25
6.005 56
3
18.1 17
4 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 on p. 6.)
Exercise 10
0.1
Exercise 11
0.53
(Solution on p. 6.)
Exercise 12
0.71
Exercise 13
0.219
(Solution on p. 6.)
Exercise 14
0.811
Exercise 15
4.8
Exercise 16
2.6
http://cnx.org/content/m34958/1.2/
(Solution on p. 6.)
OpenStax-CNX module: m34958
Exercise 17
16.12
4
(Solution on p. 6.)
Exercise 18
25.88
Exercise 19
6.0005
(Solution on p. 6.)
Exercise 20
1.355
Exercise 21
16.125
(Solution on p. 6.)
Exercise 22
0.375
Exercise 23
3.04
(Solution on p. 6.)
Exercise 24
21.1875
Exercise 25
8.225
(Solution on p. 6.)
Exercise 26
1.0055
Exercise 27
9.99995
(Solution on p. 6.)
Exercise 28
22.110
For the following 10 problems, convert each complex decimal to a fraction.
Exercise 29
0.7 12
(Solution on p. 6.)
Exercise 30
0.012 12
Exercise 31
2.16 14
(Solution on p. 6.)
Exercise 32
5.18 23
Exercise 33
14.112 13
(Solution on p. 6.)
Exercise 34
80.0011 37
Exercise 35
5
1.40 16
(Solution on p. 6.)
Exercise 36
0.8 53
Exercise 37
1.9 75
Exercise 38
1.7 37
9
http://cnx.org/content/m34958/1.2/
(Solution on p. 6.)
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4.1 Exercises for Review
Exercise 39
( here1 ) Find the greatest common factor of 70, 182, and 154.
(Solution on p. 6.)
Exercise 40
( here2 ) Find the greatest common multiple of 14, 26, and 60.
Exercise 41
( here3 ) Find the value of
3
5
·
15
18
÷ 59 .
(Solution on p. 6.)
Exercise 42
1
( here4 ) Find the value of 5 23 + 8 12
.
Exercise 43
( here5 ) In the decimal number 26.10742, the digit 7 is in what position?
(Solution on p. 7.)
1 "Exponents, Roots, Factorization of Whole Numbers: The Least Common Multiple"
<http://cnx.org/content/m34876/latest/>
2 "Exponents, Roots, Factorization of Whole Numbers: The Least Common Multiple"
<http://cnx.org/content/m34876/latest/>
3 "Introduction to Fractions and Multiplication and Division of Fractions: Multiplication of Fractions"
<http://cnx.org/content/m34928/latest/>
4 "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Addition and Subtraction of
Mixed Numbers" <http://cnx.org/content/m34936/latest/>
5 "Decimals: Reading and Writing Decimals" <http://cnx.org/content/m34957/latest/>
http://cnx.org/content/m34958/1.2/
OpenStax-CNX module: m34958
Solutions to Exercises in this Module
Solution to Exercise (p. 2)
16 21
25
Solution to Exercise (p. 2)
513
1,000
Solution to Exercise (p. 2)
6, 646 10107
,000
Solution to Exercise (p. 2)
1
1 10
Solution to Exercise (p. 3)
7
8
Solution to Exercise (p. 3)
31
250
Solution to Exercise (p. 3)
7
6 1,200
Solution to Exercise (p. 3)
2
18 17
Solution to Exercise (p. 3)
7
10
Solution to Exercise (p. 3)
53
100
Solution to Exercise (p. 3)
219
1,000
Solution to Exercise (p. 3)
4 45
Solution to Exercise (p. 4)
3
16 25
Solution to Exercise (p. 4)
1
6 2,000
Solution to Exercise (p. 4)
16 81
Solution to Exercise (p. 4)
1
3 25
Solution to Exercise (p. 4)
9
8 40
Solution to Exercise (p. 4)
,999
9 19
20,000
Solution to Exercise (p. 4)
3
4
Solution to Exercise (p. 4)
2 13
80
Solution to Exercise (p. 4)
14 3,337
000
Solution to Exercise (p. 4)
1 129
320
Solution to Exercise (p. 4)
1
2 25
Solution to Exercise (p. 5)
14
http://cnx.org/content/m34958/1.2/
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OpenStax-CNX module: m34958
Solution to Exercise (p. 5)
9
10
Solution to Exercise (p. 5)
thousandths
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