That's pretty much the same as my solution, so just a couple of things:

(1): The default precision with bignum (as I used) is good enough for up to 99, but if I want to go above, I need to use higher precision too. Your code fails even earlier. A constant div_scale of 50 only goes so far ... though of course when the list of numbers checked is also constant, I guess I can't fault it.

(2): Your code will break for numbers above 100 (even if you up the div_scale), since every float will begin with "0.00", and your code will see the repeated "0", and think it is the period ... no matter what follows it! Even if you hard code it so that you skip those initial zeros, it will find false positives for other numbers as well: 1/2048 == 0.00048828125, exact, but your code (if fixed to skip the zeros) will find a repeated digit "8" and assume it is the cycle sequence.

(I solve this problem by insisting that there are fewer than COUNT characters remaining after the match and making sure the string is big enough that we get at least two COUNTs worth of cyclying, which also requires keeping trailing zeros.)

So yeah, I guess you were still missing something. :)