P
ble-6. Write the decimal expansion of the following rational numbers without actual division
35/50,21/25,7/8
Answers
Without actual division, classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
(i) 167
(ii) 15013
(iii) 75−11
(iv) 20017
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ANSWER
(i) 16=24
167=247=24×507. So, 167 has a terminating decimal expansion.
(ii) 150=2×3×52
15013=2×3×5213
Since it is not in the form 2m×5np,15013 has a non-terminating and recurring decimal expansion.
(iii)
Answer:
ANSWER
(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.
Step-by-step explanation: