33.55 Let $D$ denote a repeating decimal. If $P$ represents the $r$ non-repeating digits of $D$, and $Q$ represents the $s$ repeating digits of $D$, then the incorrect representation is
(A) $D=0 . P Q Q \cdots \cdots$.
(B) $10^{r} \mathrm{D}=P . Q Q Q \cdots \cdots$.
(C) $10^{r+s} D=P Q \cdot Q Q Q \cdots \cdots$.
(D) $10^{r}\left(10^{s}-1\right) D=Q(P-1)$.
(E) $10^{r} \cdot 10^{2 s} \mathrm{D}=P Q Q \cdot Q Q Q \cdots \cdots$.
(3rd American High School Mathematics Examination, 1952)
[Solution] It is easy to verify that $(A),(B),(C),(E)$ are all correct. Now consider $(D)$:
$$
\begin{aligned}
\text { LHS } & =10^{r}\left(10^{s}-1\right) D=10^{r+s} D-10^{r} D \\
& =P Q \cdot Q Q \cdots \cdots-P \cdot Q Q Q \cdots \cdots \\
& =P Q-P=P(Q-1) .
\end{aligned}
$$

Therefore, the answer is $(D)$.