Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 20
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36MODULE -
1
Number Systems
Algebra
1.8 DECIMAL REPRESENTATION OF A RATIONAL
NUMBER
You are familiar with the division of an integer by another integer and expressing the result
Notes
as a decimal number. The process of expressing a rational number into decimal form is to
carryout the process of long division using decimal notation.
Let us consider some examples.
Example 1.13:
Represent each one of the following into a decimal number:
−
12
27
13
(i)
(ii)
(iii)
5
25
16
Solution:
i)
Using long division, we get
2
4 .
5
12
0 .
12
=
10
Hence,
2.4
5
2.0
2.0
×
ii)
(–1.08
25 −
27
25
–
27
=
Hence,
–
. 1
08
200
25
200
×
. 0
8125
iii)
16
13
.
0000
128
20
13
16
=
Hence,
. 0
8125
16
40
32
80
80
×
From the above examples, it can be seen that the division process stops after a finite
number of steps, when the remainder becomes zero and the resulting decimal number has
a finite number of decimal places. Such decimals are known as terminating decimals.
Note:
Note that in the above division, the denominators of the rational numbers had only
2 or 5 or both as the only prime factors.
×
12
12
2
24
=
=
as
2.4
Alternatively, we could have written
and similarly for the others
×
5
5
2
10
22
Mathematics Secondary Course
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