Let x = 0.78367836...
thus 10,000 x = 7836.7836- / you multiply both sides by 10,000 because -x = .7836 there are 4 repeating decimals
9999 x = 7836 if there are one,multiply by 10 and so on
x = 7836/9999
actually in this particular case you don't have to work out the problem . By inspection you will know the equivalent fraction is 7836/9999