Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 22
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36MODULE -
1
Number Systems
Algebra
From the above, it is clear that in cases where the denominator has factors other than 2 or
5, the decimal representation starts repeating. Such decimals are called non-terminating
repeating decimals.
Thus, we see from examples 1.13 and 1.14 that the decimal representation of a rational
Notes
number is
(i) either a terminating decimal (and the remainder is zero after a finite number of steps)
(ii) or a non-terminating repeating decimal (where the division will never end)
∴ Thus, a rational number is either a terminating decimal or a non-terminating repeating
decimal
1.8 EXPRESSING DECIMAL EXPANSION OF A RATIONAL
NUMBER IN p/q FORM
Let us explain it through examples
p
Example 1.15:
Express (i) 0.48 and (ii) 0.1357 in
form
q
48
12
=
=
. 0
48
Solution:
(i)
100
25
1375
55
11
=
=
=
. 0
1375
(ii)
10000
400
80
p
Example 1.16:
Express (i) 0.666... (ii) 0.374374... in
form
q
Solution:
(i)
Let x = 0.666...
(A)
∴ 10 x = 6.666...
(B)
2
=
x
(B) – (A) gives 9 x = 6 or
3
(ii)
Let x = 0.374374374....
(A)
1000 x = 374.374374374.... (B)
(B) – (A) gives 999 x = 374
374
=
x
or
999
24
Mathematics Secondary Course
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