AMC8 1996

AMC8 1996 · Q11

AMC8 1996 · Q11. It mainly tests Absolute value, Decimals.

Let $x$ be the number $0.\underbrace{0000\dots0000}_{1996\ zeros}1$, where there are 1996 zeros after the decimal point. Which of the following expressions represents the largest number?

设 $x$ 为小数 $0.\underbrace{0000\dots0000}_{1996\ zeros}1$，其中小数点后有 1996 个零。以下哪个表达式表示最大的数？

(A) 3 + x 3 + x

(B) 3 − x 3 − x

(D) 3/x 3/x

(E) x/3 x/3

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Since $x$ is near zero, $3+x$ and $3-x$ are near $3$. Also $3\cdot x$ and $\frac{x}{3}$ are near zero. However, $\frac{3}{x}$ is the number $$ 3\,0000\ldots 0000, $$ which is a $3$ followed by $1997$ zeros. This number is much larger than any of the other alternatives.

答案（D）：由于 $x$ 接近于 $0$，所以 $3+x$ 和 $3-x$ 都接近于 $3$。同时，$3\cdot x$ 和 $\frac{x}{3}$ 都接近于 $0$。然而，$\frac{3}{x}$ 是下面这个数 $$ 3\,0000\ldots 0000, $$ 它是一个 $3$ 后面跟着 $1997$ 个 $0$。这个数远大于其他任何选项。

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