Math 40
Section 5.5: Conversions between Fractions and Decimals
Pre-Algebra
There are two conversions that we discuss in Section 5.5:
1. Decimal  Fraction
2. Fraction  Decimal
 Type 1: Decimals that terminate with a remainder of 0.
 Type 2: Decimals that repeat a fixed pattern (Repeating Decimals).
 0.2525252525...  0.25
 –3.02547547547 3.02547
 Type 3: Decimals the need to be rounded to produce a numerical approximation.
Decimal  Fraction – Just read off the place value and don’t worry about going to Lowest Terms.
–0.67 =
2.345 =
Fraction  Decimal – Uses long division.
Type 1: Divide until you get a remainder of 0.
1.
15
2.
1
250
16
Type 2: Divide and write your answer as a repeating decimal.
3.
4.
4
15
Type 3: Divide and round your answer to the nearest …
5.
6.
25
… tenth
12
… hundredth

1
60
5
12
Additional Problems Involving Fraction/Decimal Conversions:
Compare and insert < , > , or = in the box to make a true statement
7.
Hint:
8.
7
16
0.45 
0.09  
7
 0.4375
16
Hint: 
1
11
1
 0.09090909
11
Simplify (Hint: Use fractions.)
9.
0.99 
5
6
Example #9 has been designed to be worked in
fractions, since the directions tell you to do this, and
5
 0.833333... in decimal form. Generally speaking,
6
an example that combines decimals and fractions
should be rigged so that the problem will work down
easily in both its fractional and decimal form. See
example #10 below.
10.
A better example:
1
3
 0.35 
4
8
Fraction Version
Decimal Version
1
3
 0.35 
4
8
1
3
 0.35 
4
8
Answers:
1.
–0.9375
2.
6.
7.
 0.416  0.42
0.004
>
3.
8.
0.2666666…
or 0.26
<
4.
9.
–0.0166666… 5.
or 0.016
10.
47
300
 –2.08  –2.1
39
= 0.975
40