Note: This question is base sensitive. Therefore, assume we have fixed a base $b$. By abuse of terminology, I will still use the word "decimal".
This question revolves around the period of repeating decimals. For an integer $i$, define $f(i)$ as the period of the expansion of $i^{-1}$, or $1$ if the decimal expansion of $i^{-1}$ terminates. As an example, $f(3) = 1$ or $2$, depending on $b$.
Now, the behaviour of $f$ is a delightful mix of pattern and chaos. I (think I) have found three things so far:
1) For any natural $i$, $f(i) \leq (i-1)$.
2) If $i$ divides a number of the form $b^{n-1} + 1$ or $b^n - 1$ (for applicable $n$) then $f(i) \leq n$ (I believe this to be an equality if $n$ is minimal).
3) If $i = j_1\cdot j_2$ with $j_1$ and $j_2$ coprime, then $f(i) \leq \text{lcm}(f(j_1), f(j_2))$.
Now, what I want to know is whether or not these three points are correct, and whether or not the upper bound of $f(i)$ given by these three points together is indeed the value.