write the decimal exponsion of 71/625 and 9/80 without actual division .
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(i) 16=2
4
16
7
=
2
4
7
=
2
4
×5
0
7
. So,
16
7
has a terminating decimal expansion.
(ii) 150=2×3×5
2
150
13
=
2×3×5
2
13
Since it is not in the form
2
m
×5
n
p
,
150
13
has a non-terminating and recurring decimal expansion.
(iii)
75
−11
=
3×5
2
−11
Since it is not in the form
2
m
×5
n
p
.
75
−11
has a non-terminating and recurring decimal expansion.
(iv)
200
17
=
8×25
17
=
2
3
×5
2
17
. So
200
17
has a terminating decimal expansion.
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