Example 1 Convert the rational number $\frac{67}{29}$ to a continued fraction.
Explanation: Since $\frac{67}{29}=2+\frac{9}{29}, \frac{29}{9}=3+\frac{2}{9}$, $\frac{9}{2}=4+\frac{1}{2}$, therefore,
$$
\begin{array}{l}
\frac{67}{29}=2+\frac{1}{3+\frac{1}{4+\frac{1}{2}}}=2+\frac{1}{3}+\frac{1}{4}+\frac{1}{2} \\
=[2,3,4,2] .
\end{array}
$$