Math 81
Activity # 17
“Converting between Fractions and Decimals”
Your Name: ___________________ Team Member #1__________________
Team Member #2.______________ Team Member #3__________________
Task 1: Convert a decimal to a fraction.
Note: The Key is to read the decimal as you would write the decimal notation in
words.
Problem 1: Convert the decimal 0.6 to a
fraction.
Problem 2: Convert the decimal 4.75 to a
fraction.
Solution:
Solution: 4.75 is read as four and
seventy-five hundredths, which refer
75
to the mixed number 4
. In simplest
100
75
25  3
3
4
 4 . As a
form, 4
100
25  4
4
3 19
19
fraction 4 
, so 4.75  .
4 4
4
0.7 is read as seven-tenths,
7
and in fraction form it is .
10
7
Hence, 0.7 
10
Problem 3: Convert the decimal 0.42 to a fraction.
a) 0.42 is read as ____________________
b) Write it in fraction form _________
c) Can it be simplified? ________. If so, what is the fraction
in simplest form: __________(Show your work below)
d) Therefore, 0.42 
Convert each of the following decimals to a fraction in simplest form.
1)
2) 0.785
3) 8.42
0.17
Problem 4: Convert the decimal 0.15
Solution:
0.15
7
to a fraction
8
7
is read as fifteen and seven eighths hundredths, and in fraction
8
form it is
7 127
15
8  8 Since the fraction bar represents division, we may rewrite it using the division symbol 
100 100
127

 100
8
127 1


8 100
127

800
Convert the following decimal to a fraction.
4)
0.16
2
3
Task 2: Convert a fraction to a decimal.
Note: To convert a fraction to a decimal. The Key is to divide. Then, round the
decimal to the indicated place value.
Problem 5:Convert the fraction
decimal.
7
8
to a Problem 6:Convert the fraction
to
40
3
decimal. Round to the nearest
hundredth.
Solution:
Since the fraction bar represents
7
 7  40 .
division, we have
40
So, we will take 7 divided by 40.
Solution:
Again since the fraction bar represents
8
division, we have  8  3 . So we will take 5
3
divided by 6. Using long division, we
Using long division, we have 40 7 , which
have 3 8 , which the same is
is the same as 40 7.000
0.175
40 7.000
40
300
28 0
200
200
0
Hence,
7
 0.175
40
2.666
3 8.000
6
20
18
20
18
20
18
2
Now rounding 2.666 to the nearest
8
hundredth, we get 2.67. Hence,  2.67
3
Problem 7: Convert the fraction 2
5
to a decimal. Round to the nearest
6
thousandths.
Solution:
Solution:
Method 1: Since 2
5 17

 17  6 , using
6 6
long division we will take 17 divided by 6.
2.8333
6 17.0000
Method 2: Since 2
12
50
48
20
18
20
18
2
Now rounding 2.8333 to the nearest
thousandth, we have 2.833 . Hence,
5
2  2.833
6
48
20
18
20
18
20
18
2
Now rounding 0.8333 to the nearest
thousandth, we have 0.833 . Hence,
5
5
2  2   2  0.8333  2.8333
6
6
5
5
 2  , using long
6
6
division we will take 5 divided by 6.
0.8333
6 5.0000
Tip: When converting a fraction to a decimal with a denominator that is a multiple
of 10 such as 10, 100, 1000, etc., division is not necessary. In other words, the
decimal notation can be obtained by reading as you would write the fraction in
words.
7
Example: Convert the fraction
to a decimal.
100
7
Solution:
is read as “seven hundredths”. In decimal form it is 0.07 .
100
Convert the following fractions to a decimal. Round to the nearest thousandth
when necessary.
23
27
5)
6)
4
1000
7)
5
12
8)
4
7
9
Task 3: To identify the order relation between a decimal and a fraction.
5
Problem 6: Place the correct symbol, < or >, between the numbers
and 0.312 .
16
Solution:
5
5
Convert
to a decimal by dividing  0.3125 .
16
16
Note that 0.312  0.3120 . So comparing the two decimals, we have
0.3125  0.3120
5
 0.312
Hence,
16
Place the correct symbol, <, =, or >, between the numbers.
5.08_____5.80
9) 3.08_____3.082
10)
11)
7
_____0.583
12
12)
5
_____0.2083
24
Convert each of the following decimals to a fraction in simplest form.
13)
14)
15)
0.36
4.125
0.270
16)
0.12
2
3
17)
0.025
18)
0.09
2
7
Convert each of the following fractions to a decimal. Round to the nearest
hundredth.
2
7
19)
20)
13
6
21)
12
5
6
22)
75
1000