Decimal expansion of rational numbers is terminating
or non – terminating but repeating.
Example:
3.5,
7.272727…,
3.142857142857…,
25,
3.5
=
=
47.1245
=
=
0.222
=
=
3.5 can be expressed
as i.e
P
Q
35
10
Terminating decimal expansion
Sol.
Q.1
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i)
13
3125
=
13
55
=
20
×
55
13
(ii)
17
8
=
17
23
=
23
×
50
17
has terminating decimal expansion.
13
3125
∴
has terminating decimal expansion.
17
8
∴
13
3125
17
8
Since denominator is in the form of 2n5m
Since denominator is in the form of 2n5m
(iii)
15
1600
=
3
320
=
26
×
51
3
(iv)
77
210
=
11
30
=
2
×
3
11
has terminating decimal expansion.
15
1600
∴
has non - terminating decimal expansion.
77
210
∴
15
1600
77
210
Since denominator is in the form of 2n5m
Since denominator is not in the form of 2n5m
Sol.
Q.1
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
×
5
3
320
11
30
(v)
64
455
=
5
×
7
64
(iv)
23
2352
has non-terminating repeating decimal expansion.
64
455
∴
has terminating decimal expansion.
23
2352
∴
64
455
23
2352
Since denominator is not in the form of 2n5m
Since denominator is in the form of 2n5m
×
13
455
5
7
1
13
1
3
9
1
Sol.
Q.1
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: