In the given multiplication, different letters represent different integers ranging from 0 to 9 .
G9.1 Find $A$.
G9.2 Find $B$.
G9.3 Find $C$.
G9.4 Find $D$.
$$
\begin{array}{l}
\text { A B C D } \\
\begin{array}{r} 
\\
\times \quad 9 \\
\hline \mathrm{D} \mathrm{C} \mathrm{B} \mathrm{A}
\end{array} \\
1 \text { B C } 9 \\
\begin{array}{lllll}
\times & & & & 9 \\
\hline & & & & \\
\hline 9 & \text { C B } & 1
\end{array} \\
\end{array}
$$
As there is no carry digit in the thousands digit multiplication, $\mathrm{A}=1, \mathrm{D}=9$
Consider the tens digit: $9 \mathrm{C}+8 \equiv \mathrm{B}(\bmod 10)$ $\qquad$
As there is no carry digit in the thousands digit, let the carry digit in the hundreds digit be $x$.
$9 \mathrm{~B}+x=\mathrm{C}$ and $\mathrm{B}, \mathrm{C}$ are distinct integers different from 1 and 9
$$
\begin{array}{l}
\Rightarrow B=0, C=x \\
\text { Sub. } B=0 \text { into }(1): 9 C+8 \equiv 0(\bmod 10) \\
\Rightarrow 9 C \equiv 2(\bmod 10) \\
\Rightarrow C=8 \\
\therefore A=1, B=0, C=8, D=9
\end{array}
$$