| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] 29/9261 will have a non-terminating repeating decimal expansion. |
| Reason [R] Let a = p/q be a rational number such that p and q are co-prime and the prime factorization of q is of the form\[{{2}^{n}}\times {{5}^{m}}\], where n and m are non-negative integers (whole numbers). |
| Then, a has a decimal expansion, which is non-terminating repeating. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: C
Solution :
| Given number \[=\frac{29}{9261}=\frac{29}{{{3}^{3}}\times {{7}^{3}}}\] |
| \[9261={{3}^{3}}\times {{7}^{3}}\] is not of the form |
| \[{{2}^{n}}\times {{5}^{m}}\]. Hence, \[\frac{29}{9261}\] |
| , is non-terminating repeating decimal expansion. Assertion is true but Reason is false. |
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