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Solution


Q.

Assertion (A): 15/1600 is a terminating decimal fraction.
Reason (R): If x = p/q is a rational number, such that the prime factorisation of q is of the form 2n5m,
where n, m are non-negative integers, then x = p/q is a terminating decimal fraction.
1 Both A and R are true, and R is the correct explanation of A.  
2 Both A and R are true, but R is not the correct explanation of A.
 
3 A is true, but R is false.  
4 A is false, but R is true  

Ans.

(1)

For Assertion (A)
We have, 15/1600 = 15 / (2 × 2 × 2 × 2 × 2 × 5 × 5) = 15 / (2? × 5²)
⇒ The prime factorisation of denominator 1600 of 15/1600 is of the form 2?5?, where n, m are non-negative integers.
So, 15/1600 is a terminating decimal fraction.
Hence, Assertion (A) is true.
Also Reason (R) is true because it is the statement of a known theorem which says
“If x = p/q is a rational number, such that the prime factorisation of q is of the form 2?5?, where n, m are non-negative integers,
then x = p/q is a terminating decimal fraction.”
Also, it helps to prove Assertion (A) and so Reason (R) is the correct explanation of Assertion (A).