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Answers
Answer:-
1) b. 21/5^6×2^3
2) b. 1000
3) d. 1
4) a. Rational number
5) c. 6
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Answer:
Option b - \frac{21}{2^35^6}
2
3
5
6
21
is terminating.
Step-by-step explanation:
To find : Which of the following numbers has terminating decimal expansion ?
Solution :
A rational number terminates only when its denominator is in the form 2^m\times 5^n2
m
×5
n
and doesn't include any other prime factor in it's standard form.
Now, We factories the denominator to get in the form
a) \frac{37}{45}
45
37
\frac{37}{45}=\frac{37}{3^2\times 5^1}
45
37
=
3
2
×5
1
37
It is not terminating.
b) \frac{21}{2^35^6}
2
3
5
6
21
\frac{21}{2^3\times 5^6}
2
3
×5
6
21
It is terminating.
c) \frac{17}{49}
49
17
\frac{17}{49}=\frac{17}{7^2}
49
17
=
7
2
17
It is not terminating.
d) \frac{89}{2^33^2}
2
3
3
2
89
\frac{89}{2^3\times 3^2}
2
3
×3
2
89
It is not terminating.
