I'm in the wrong room, but I'm trying to keep from getting my comments moved down here by a moderator. Your comments about 1/7 hold for any fraction of the form 1/(p-1). where p is an odd prime whose decimal representation repeats in exactly p-1 steps (1/7 =142857...) The next such prime is 17 (1/17 = .0588235294117647...) Once you know the first p-1 digits, the rest just add to 9 (e.g. for 1/7 1+8; 4+5; 2+7 so from 142 you get 857. It is unknown if there are infinitely many such primes.