$13/92=0.14\overline{1304347826086956521739}$
In this example, the length of nonrepeating part is $2$. The length of repeating part (repeating period) is $22$.
I collected some properties related to repeating decimals.
- The repeating period must be less than divisor.-- It doesn't give me the exact period.
- If divisor d is a multiple of $2^m 5^n$, the length of non-repeating part of $1\div d$ is $\max(m,n)$. -- It only applies to $1\div d$.
- If $1 \leqslant b < a$, and $a$ is not a multiple of $2$ or $5$, and $a$ and $b$ are relatively prime, then the repeating period of $b\div a$ equals $\operatorname{min}\left \{ e\in \mathbb{N}:10^e\equiv 1 \pmod{a} \right \}$. -- It has many conditions.
Without calculating the decimal, can we determine the length of the two parts of any dividend and divisor?