# 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 $\frac19, \frac{1}{99}, \frac{1}{999}, \frac{1}{9999},\ldots$