Question

令 $x$ 为数

$0.\underbrace{0000\ldots00001}_{1996 \text{ 个零}}\text{，}$

其中小数点后有 $1996$ 个零。下列哪个表达式表示最大的数？

Let $x$ be the number

$0.\underbrace{0000\ldots00001}_{1996 \text{ zeros}},$

where there are $1996$ zeros after the decimal point. Which of the following expressions represents the largest number?

$3 + x$

$3 - x$

$3 \cdot x$

$\frac{3}{x}$

$\frac{x}{3}$

知识点：估算

$x$ 是一个非常小的正数，刚刚大于 $0$ 。

$x$ is a tiny positive number, just above $0$

用 $3$ 除以一个很小的数会得到巨大结果，而其他选项都接近 $3$ 或接近 $0$ 。

Dividing $3$ by a tiny number gives a huge result, while the other choices stay near $3$ or near $0$

因为 $x$ 是很小的正数， $3 + x$ 和 $3 - x$ 都接近 $3$ ，而 $3 \cdot x$ 和 $\frac{x}{3}$ 都接近 $0$ 。

但 $\frac{3}{x}$ 是 $3$ 后面跟着 $1997$ 个零，远大于其他选项。

所以正确答案是 D。

Since $x$ is a very small positive number, $3 + x$ and $3 - x$ are near $3,$ while $3 \cdot x$ and $\frac{x}{3}$ are near $0.$

But $\frac{3}{x}$ is $3$ followed by $1997$ zeros, far larger than any other choice.

Thus, the correct answer is D .