Is there an algorithm for figuring out the following things?

1. If the result of a division is a repeating decimal (in binary).
2. If it repeats, at what digit (represented as a power of 2) does the repetition start?
3. What digits repeat?

Some examples:

```
1/2 = 1/10 = 0.1 // 1 = false, 2 = N/A, 3 = N/A, 4 = N/A
1/3 = 1/11 = 0.010101... // 1 = true, 2 = -2, 3 = 10
2/3 = 10/11 = 0.101010... // 1 = true, 2 = -1, 3 = 10
4/3 = 100/11 = 1.010101... // 1 = true, 2 = 0, 3 = 10
1/5 = 1/101 = 0.001100110011... // 1 = true, 2 = -3, 3 = 1100

```

Is there a way to do this? Efficiency is a big concern. A description of the algorithm would be preferred over code, but I'll take what answer I can get.

It's also worth noting that the base isn't a big deal; I can convert the algorithm over to binary (or if it's in, say base 256 to use `char`s for ease, I could just use that). I say this because if you're explaining it might be easier for you to explain in base 10 :).