Example 2 (2004 Jiangsu Summer Camp) Given the function $f(n)=k$, where $k$ is the $n$-th digit after the decimal point of the repeating decimal $0 . \dot{9} 1827364 \dot{5}$, then the value of $\underbrace{f\{f \cdots f[f(1)]\}}_{200 \uparrow f}$ is
A. 9
B. 8
C. 7
D. 3
Solution: It is easy to get $f_{9 s+t}(1)=f_{t}(1), s, t \in \mathbf{N}^{*}$, $f_{2004}(1)=f_{6}(1)=8$, choose $(\mathrm{B})$.