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MathNet 2015-part-03 — 191 problems (EN–VI) Question 90

Math Olympiad Vault · MathNet 2015-part-03 — 191 problems (EN–VI)

Question 90

For any natural number $n \gt 1$, write the infinite decimal expansion of $1 / n$ (for example, we write $1 / 2 = 0.4\overline{9}$ as its infinite decimal expansion, not $0.5$). Determine the length of the non-periodic part of the (infinite) decimal expansion of $1 / n$.