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IMO LongList 1967, The Democratic Republic Of Germany 2

Source: IMO LongList 1967, The Democratic Republic Of Germany 2

December 16, 2004
number theoryapproximationdecimal representationrational numberirrational numberIMO ShortlistIMO Longlist

Problem Statement

Which fractions pq, \dfrac{p}{q}, where p,qp,q are positive integers <100< 100, is closest to 2?\sqrt{2} ? Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of 2\sqrt{2} (without using any table).
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