alleryFor which of the following fractions will the decimal expansion have a REPEATING (non-terminating) block?
A7/8
B3/25
C13/16
D2/15
Answer & Solution
Correct answer: D. 2/15
A p/q (in lowest terms) terminates iff q's prime factorisation contains only 2 and/or 5. Check: 8 = 2³ (terminates: 7/8 = 0.875).
25 = 5² (terminates: 3/25 = 0.12).
16 = 2⁴ (terminates: 13/16 = 0.8125).
15 = 3·5 (has a 3 — repeats!).
2/15 = 0.13333… is non-terminating repeating.
**Answer:** 2/15.
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