Part BCSIR NET June 2025terminating-decimals-need-denominator-2n5m-not-just-2n

Terminating decimals need denominator 2n5m not just 2n

Let A = { $p / q \in (0, 1) : p \in N, q = 2^{n}$ for some $n \in N \cup$ {0}, gcd(p, q) = 1}, B = { $p / q \in (0, 1) : p \in N, q = 2^{n} 5^{m}$ for some $n, m \in N \cup$ {0}, gcd(p, q) = 1} and C = {p/q ∈ (0, 1) : p/q has terminating decimal expansion} be subsets of (0, 1). Which of the following statements is true?

A.A ⊊ C and B ⊊ C
B.A ⊊ C ⊊ B
C.A ⊊ B ⊊ C
D.A ⊊ B = C✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

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Terminating decimals need denominator 2n5m not just 2n

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