Which of the following rational numbers will have a non - terminating repeating decimal expansion *
35/25
10/125
7/6
21/4
Answers
Answer:
7/6,because it is ending in the form 3*2 and not in the form 2^m * 5^n
therefore non terminating and recurring
Step-by-step explanation:
Answer:
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Hence option (D) has a non terminating repeating decimal expansion.
D none of these.
Step-by-step explanation:
Given:
A) 31/3125
B) 71/512
C)23/200
D) none of these
We know that a rational number has a terminating decimal expansion, if the prime factorisationof the denominator is of the form of 2^m 5^n2
m
5
n
, where m and n are non negative integers.
Now solving one by one.
A) \frac{31}{3125}=\frac{31}{5\times5\times5\times5\times5}
3125
31
=
5×5×5×5×5
31
= \frac{31}{5^52^0}
5
5
2
0
31
So, given number has terminating decimal expansion.
B) \frac{17}{512}=\frac{17}{2\times2\times2\times2\times2\times2\times2\times2\times2\times2}
512
17
=
2×2×2×2×2×2×2×2×2×2
17
=\frac{17}{2^95^0}
2
9
5
0
17
So, given number has terminating decimal expansion.
C)\frac{23}{200}=\frac{23}{2\times2\times2\times5\times5}
200
23
=
2×2×2×5×5
23
=\frac{23}{2^35^2}
2
3
5
2
23
So, given number has terminating decimal expansion.
Hence option (D) has a non terminating repeating decimal expansion.
D none of these.