Two statements are given: Statement I : The sum of exponents of prime factors in the prime factorization of 392 is 5. Statement II : The decimal representation \(\frac{13}{2^3 \times 5}\) will…
Question and options
Two statements are given:
Statement I : The sum of exponents of prime factors in the prime factorization of 392 is 5.
Statement II : The decimal representation will terminate after 2 decimal places.
In the light of the given statements, choose the correct answer from the given options:
Statement I : The sum of exponents of prime factors in the prime factorization of 392 is 5.
Statement II : The decimal representation will terminate after 2 decimal places.
In the light of the given statements, choose the correct answer from the given options:
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but Statement II is false
- Statement I is false but Statement II is true
Answer and explanation
Correct answer: C - Statement I is true but Statement II is false
392 = 2^3 x 7^2, so the exponents sum to 5 (I true). 13/(2^3 x 5) = 13/40 = 0.325, which terminates after 3 decimal places, not 2 (II false).
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