Which fractions where are positive integers , is closest to Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of (without using any table).
%V0
Which fractions $\displaystyle \dfrac{p}{q},$ where $p,q$ are positive integers $< 100$, is closest to $\sqrt{2} ?$ Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of $\sqrt{2}$ (without using any table).
Source: Međunarodna matematička olimpijada, shortlist 1967
Školjka 
where 
are positive integers 
, is closest to 
Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of 
(without using any table).