9.8. Ji Ma calculated the reciprocal of the factorial of each integer from $80 \sim 99$, and printed the resulting decimal fractions on 20 infinitely long strips of paper (for example, Sasha cut a segment from one of the strips, which had exactly $n$ digits without a decimal point. If Sasha does not want Ji Ma to guess which strip the $n$ digits were cut from, what is the maximum value of $n$?
9.8. The maximum value of $n$ is 155.

Assuming that on the slips of paper, $\frac{1}{k!}$ and $\frac{1}{l!}$ (where $k < l$) are written, the first 156 digits of the decimal expansion of $\frac{1}{k!} - \frac{1}{l!}$ are greater than $\frac{1}{10^{16}}$. Therefore, $n < 156$.

Thus, for any segment of 156 digits, we can determine its origin. However, when $n = 155$, on the slips of paper with $\frac{1}{98!}$ and $\frac{1}{99!}$, there is a completely identical segment of 155 digits:
$$
\begin{array}{l}
=0 . \underbrace{00 \cdots 0106 \cdots}_{153 \uparrow} \text {, } \\
\end{array}
$$