CCBC Math 081
Third Edition
Converting between Decimals and Fractions
Section 4.2
7 pages
4.2 Converting between Decimals and Fractions
In the introduction, we talked about how $2.75 represents two whole dollars plus 75 cents, which
is a fractional part of another whole dollar. Since it takes 100 cents to make a dollar, 75 cents
can be written in fraction form as
equivalent to 2
75
3
which reduces to . So, 2.75 in decimal form is
4
100
3
in fraction form.
4
Let’s look at some fractions using powers of 10 to see their connection to decimal place values.
Dividing 1 into 10 equal parts gives us tenths; a tenth can be represented as
1 tenth =
1
.
10
1
as a fraction = 0.1 as a decimal
10
Dividing 1 into 100 equal parts gives us hundredths; a hundredth can be represented as
1 hundredth =
1
.
100
1
as a fraction = 0.01 as a decimal
100
Dividing 1 into 1000 equal parts gives us thousandths; a thousandth can be represented as
1 thousandth =
1
.
1000
1
as a fraction = 0.001 as a decimal
1000
Notice that the number of 0s in the denominator of the fraction is equal to the number of places
to the right of the decimal point where the digit 1 is located in the decimal number.
Converting from a Decimal to a Fraction
We will learn how to convert decimals into fractions using the place value of the digits in the
decimal number.
276
CCBC Math 081
Third Edition
Example 1:
Converting between Decimals and Fractions
Section 4.2
7 pages
Represent the decimal 6.37 as a fraction.
The digit 6 is in the ones place and represents six ones or six ―wholes‖.
The digit 3 is in the tenths place so the 3 represents
3
.
10
The digit 7 in the hundredths place so the 7 represents
We can write 6.37 as 6 
7
.
100
3
7
. To add fractions, we need a common denominator, which

10 100
will be 100:
6 3
7
 
1 10 100
6  100 3  10
7



1 100 10  10 100
600 30
7



100 100 100
637

100
637
37
6.37 
6
100
100

Answer:
Let’s look at 6
Rewrite the whole numbers over one.
Determine what to multiply by to get 100.
Multiply.
Add the numerators together.
37
a little more closely. Since the rightmost place of 6.37 is the hundredths
100
place, it makes sense that the denominator of the fraction is 100 as well. All we really need to
do to convert a decimal to a fraction is determine the number of digits to the right of the
decimal point. An easy way to do this is to see that there are two digits to the right of the
decimal point in 6.37, corresponding to the two zeros in the denominator of 6
Practice 1:
Represent 2.7 as a fraction in simplest form.
Watch It:
http://youtu.be/SSJfeMtndpY
277
Answer:
37
.
100
27
7
2
10
10
CCBC Math 081
Third Edition
Example 2:
Converting between Decimals and Fractions
Section 4.2
7 pages
Represent the decimal 23.571 as a fraction in simplest form.
Since the rightmost decimal place is the thousandths place, the denominator will be 1,000.
Similarly, we can reason that because there are three digits to the right of the decimal point,
there should be three zeros (in the power of 10) in the denominator, giving us the denominator
1,000.
Answer:
23.571 
23571
571
or 23
1000
1000
Note that this fraction is in simplest terms and cannot be reduced.
It is okay to leave the conversion as an improper fraction as long as it is in simplest form.
Practice 2:
Represent 39.201 as a fraction in simplest form.
Watch It:
http://youtu.be/6hoFx6vMi9Y
Example 3:
Represent the decimal 0.10412 as a fraction in simplest form.
Answer:
39201
201
 39
1000
1000
Since the rightmost decimal place is the hundred thousandths place, the denominator will be
100,000. Similarly, we can reason that because there are five digits to the right of the decimal
point, there should be five zeros (in the power of 10) in the denominator, giving us the
denominator 100,000. So:
10412
which reduces to
100000
10412  2
5206
5206  2
2603




100000  2 50000 50000  2 25000
0.10412 
2603
25000
Answer:
0.10412 
Practice 3:
Represent 0.495 as a fraction in simplest form.
Watch It:
http://youtu.be/lWXN-c2I7Lk
278
Answer:
99
200
CCBC Math 081
Third Edition
Converting between Decimals and Fractions
Section 4.2
7 pages
Converting from a Fraction to a Decimal
Note: In this section we will work only with fractions having denominators easily changed to a
power of 10. Later in the chapter, you will learn more skills allowing you to convert any fraction
to a decimal.
We should be able to convert a fraction to decimal form using the same idea as above.
Example 4:
Represent the fraction
27
as a decimal.
100
Since the denominator is 100, the hundredths place must contain the rightmost digit of 27,
which is 7. Thus, 0.27 is the decimal form. Notice we would read both the fraction and the
decimal as ―27 hundredths‖.
We could also reason that since the power of 10 in the denominator—100 in this fraction—has
two zeroes, there should be two digits to the right of the decimal point.
Answer:
27
 0.27
100
Practice 4:
Represent the fraction
Watch It:
http://youtu.be/kt9h_Wz-yhQ
Example 5:
Represent the fraction
352
as a decimal.
10000
Answer: 0.0352
1043
as a decimal.
10
Since the denominator is 10, the tenths place must contain the rightmost digit of 1043, which is
3. Thus, 104.3 is the decimal form. We could also reason that since the power of 10 in the
denominator—10 in this fraction—has one zero, there should be just one digit to the right of the
decimal point. Thus, 104.3 is the decimal form.
1043
 104.3
10
1043
Notice that the numerator of
is greater than the denominator, which means that the
10
Answer:
fraction is greater than or equal to 1 in value. Thus, there will be at least one nonzero digit to the
left of the decimal point in the decimal conversion of the fraction. Also, we could write
1043
3
 104 . Read both the fraction and the decimal as ―one hundred four and three tenths‖.
10
10
973
Practice 5: Represent the fraction
as a decimal.
Answer: 9.73
100
Watch It:
http://youtu.be/tvk9ouRqX0w
279
CCBC Math 081
Third Edition
Example 6:
Converting between Decimals and Fractions
Represent the fraction
Section 4.2
7 pages
7
as a decimal.
20
We will have to begin this example a little differently than Examples 4 and 5, because the
denominator is not a power of 10 (10 or 100 or 1000, etc.). Fortunately, 20 is a factor of 100;
Multiply both the numerator and denominator by 5 to write an equivalent fraction with a
denominator of 100. Then write ―35 hundredths‖ as 0.35:
7
75
35


 0.35
20 20  5 100
Answer:
7
= 0.35
20
Practice 6:
Represent the fraction
Watch It:
http://youtu.be/AAMw9d4mXd8
4
as a decimal.
5
Answer: 0.8
Calculator Note
Converting from a fraction to a decimal by hand helps us understand the connection between
fractions and decimals. We can also use our calculator to convert. Start by rewriting the fraction
as a division problem. Then, use the calculator to perform that division, remembering to enter
the numerator first.
For example, to represent the fraction
7  20 on the calculator to get 0.35.
7
7
as a decimal, read
as ―7 divided by 20‖ and enter
20
20
Watch All: http://youtu.be/rSLk9zrgszo
280
CCBC Math 081
Third Edition
Converting between Decimals and Fractions
4.2 Converting Between Decimals and Fractions Exercises
In Exercises 1 – 10, represent each decimal as a fraction in simplest form.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
203.27
0.1034
74.1005
9.31
0.571
1.3002
405.3
0.44
3.5
12.123
In Exercises 11 – 20, represent each fraction as a decimal.
11.
73
100
12.
241
10
13.
517
10000
14.
1073
10
15.
407
100
16.
9
1000
17.
13
1000
18.
1
4
19.
3
5
20.
17
500
281
Section 4.2
7 pages
CCBC Math 081
Third Edition
Converting between Decimals and Fractions
4.2 Converting Between Decimals and Fractions Exercises Answers
1.
20327
27
or 203
100
100
2.
1034
517

10000 5000
3.
741005 148201
201

or 74
10000
2000
2000
4.
931
31
or 9
100
100
5.
571
1000
6.
13002 6501
1501

or 1
10000 5000
5000
7.
4053
3
or 405
10
10
8.
44 11

100 25
9.
35 7
1
 or 3
10 2
2
10.
12123
123
or 12
1000
1000
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
0.73
24.1
0.0517
107.3
4.07
0.009
0.013
0.25
0.6
0.034
282
Section 4.2
7 pages