Example 5 Let $R_{x}$ denote the positive integer in decimal notation consisting of $x$ ones. Determine whether $Q=\frac{R_{24}}{R_{4}}$ is a decimal number consisting of several 1s and 0s, and find the number of 0s in $Q$.
(44th American High School AHSME)
Solution: By reversing the formula for the sum of a geometric series, we have
$$
\begin{aligned}
Q & =\frac{R_{24}}{R_{4}}=\frac{9 R_{24}}{9 R_{4}} \\
& =\frac{10^{24}-1}{10^{4}-1}=\frac{\left(10^{4}\right)^{6}-1}{10^{4}-1} \\
& =10^{20}+10^{16}+10^{12}+10^{8}+10^{4}+1 \\
& =100010001000100010001 .
\end{aligned}
$$

Therefore, $Q$ contains 15 zeros.