a) Calculate the decimal expansion of 1/51 longhand (painful but it's good for the soul), then note that the expansion will (probably) repeat after 5, or 10, or 25, etc. numbers.
b) Multiply that expansion by 2, then 3, etc. till you see what pattern emerges.
c) Look at the patterns in what you got.
At worst this means a lot of manual calculation unless you have a hefty piece of software that goes to lots of digits.
I know hand calculation is unfashionable nowadays, but so is walking.