without actual division determine which of the following rational numbers have a terminating decimal representation and which have a non terminating decimal representation 15/11
Answers
Answer:
The rational not having denominator as multiple of 2
m
×5
n
will be non terminating.
(1)
16
7
=
2×2×2×2
7
− denominator is multiple of 2
m
×5
n
hence terminating.
(2)
125
23
=
5×5×5
23
-- denominator is multiple of 2
m
×5
n
hence terminating.
(3)
14
9
=
7×2
9
-- denominator is not multiple of 2
m
×5
n
hence non-terminating
(4)
45
32
=
3×3×5
32
-- denominator is not multiple of 2
m
×5
n
hence non-terminating.
(5)
50
43
=
5×5×2
43
-- denominator is multiple of 2
m
×5
n
hence terminating.
(6)
40
17
=
2×2×2×5
17
-- denominator is multiple of 2
m
×5
n
hence terminating.
(7)
75
61
-- denominator is not multiple of 2
m
×5
n
hence non-terminating.
(8)
250
123
=
5×5×5×2
123
-- denominator is multiple of 2
m
×5
n
hence terminating.
(i), (ii), (v), (vi) and (viii) will have terminating decimal.