The numbers 123456789 and 999999999 are multiplied. How many of the digits in the final result are 9's?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 17
The numbers 123456789 and 999999999 are multiplied. How many of the digits in the final result are 9 's?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 17

## Solution

Rewrite the product as follows:

$$
\begin{aligned}
& (123456789)(999999 \quad 999)=(123456789)\left(10^{9}-1\right) \\
& =\left(\begin{array}{lll}
123 & 456 & 789
\end{array}\right) \times 10^{9}-\left(\begin{array}{lll}
123 & 456 & 789
\end{array}\right)
\end{aligned}
$$

When 123456789 is subtracted from (123 456789$) \times 10^{9}$ the result is 123456788876543211 . None of the digits are 9's.

ANSWER: (A)