A Smallest-Denominator Fraction

Problem

A fraction $\dfrac pq$ (with $p,q$ positive integers) has decimal expansion $\dfrac pq=0.198\ldots$ (that is, its decimal begins $0.198$ ). When $q$ is as small as possible, find $p+q$ .

Answer

Solution

Difficulty	7/10
Topics	number theory, Estimation

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