Let $x$ be the number
\[0.\underbrace{0000...0000}_{1996\text{ zeros}}1,\]
where there are 1996 zeros after the decimal point.  Which of the following expressions represents the largest number?
$\text{(A)}\ 3+x \qquad \text{(B)}\ 3-x \qquad \text{(C)}\ 3\cdot x \qquad \text{(D)}\ 3/x \qquad \text{(E)}\ x/3$
Estimate each of the options.
$A$ will give a number that is just over $3$.
$B$ will give a number that is just under $3$.  This eliminates $B$, because $A$ is bigger.
$C$ will give a number that is barely over $0$, since it is three times a tiny number.  This eliminates $C$, because $A$ is bigger.
$D$ will give a huge number.  $\frac{1}{x}$ will get very, very large in magnitude when $x$ gets close to zero.  You can see this by examining the sequence $x=0.1$, which gives $10$ as the reciprocal, $x=0.01$, which gives $100$ as the reciprocal, and $x=0.001$, which gives $1000$ as the reciprocal.  Thus, $D$ will be huge, and this eliminates $A$.
$E$ will give a small number, since you're dividing a tiny number into thirds.  This eliminates $E$, and gives $\boxed{D}$ as the answer.