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m/n =0.167a_1a_2... where n <=100 is wrong

Source: Singapore Junior Math Olympiad 2010 2nd Round p4 SMO

March 26, 2020
number theoryFraction

Problem Statement

A student divides an integer mm by a positive integer nn, where n≤100n \le 100, and claims that mn=0.167a1a2...\frac{m}{n}=0.167a_1a_2... . Show the student must be wrong.
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