If $a$ is the number $0, \underbrace{000 \ldots 000}_{2009 \text { zeros }} 1$, then which of the following expressions represents the largest number?
(A) $3+a$
(B) $3-a$
(C) $3 a$
(D) $3 / a$
(E) $a / 3$
The correct answer is (D).

Let's try to compare the 5 numbers without performing calculations. We have:

$$
\begin{aligned}
3+a= & 3.000 \ldots 0001 \text { is less than } 4 \\
3-a & \text { is less than } 3 \\
3 a= & 0.000 \ldots 0003 \text { is less than } 1 \\
\frac{3}{a}= & \frac{3}{0.000 \ldots 0001}=\frac{3}{\frac{1}{10^{2010}}}=3 \times 10^{2010} \text { is greater than } 10 \\
\frac{a}{3}= & \frac{0.000 \ldots 0001}{3} \text { is less than } 0.000 \ldots 0001
\end{aligned}
$$

Therefore, the largest number is $\frac{3}{a}$.