Reciprocals and repeating digits

1. Oct 27, 2013

guysensei1

So when you take the reciprocals of integers, some have nice non repeating decimal forms like 0.5 and 0.2, but of course a lot of them give infinite repeating strings.

1/7 gives 0.142857 repeating, so there are 6 digits repeating.
1/12 give 0.083333... but there is only 1 digits that's repeating, which is 3.

Which integer reciprocal gives the most digits repeating? Or is there no answer?

2. Oct 28, 2013

pwsnafu

Consider the sequence $\frac19, \frac{1}{99}, \frac{1}{999}, \frac{1}{9999},\ldots$