Basic Analysis I — Real Analysis · Problem 1.5.7

Real Numbers — Jiri Lebl

Mathematics — Real Analysis · decimal-representation

Problem

Prove that if x=p/q∈(0,1]x = p/q \in (0, 1] is a rational number, q>1q > 1, then the period PP of repeating digits in the decimal representation of xx is in fact less than or equal to q−1q - 1.

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