AMC10 2001 A

AMC10 2001 A · Q7

AMC10 2001 A · Q7. It mainly tests Quadratic equations, Decimals.

When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number?

将某个正小数的十进制点向右移动四位后，新数字是原数字倒数的四倍。原数字是多少？

(A) 0.0002 0.0002

(B) 0.002 0.002

(D) 0.2 0.2

(E) 2 2

Answer

Correct choice: (C)

正确答案：（C）

Solution

If $x$ is the number, then moving the decimal point four places to the right is the same as multiplying $x$ by 10,000. That is, $10,000x = 4 \cdot (\frac{1}{x})$, which is equivalent to $x^2 = 4/10,000$. Since $x$ is positive, it follows that $x = 2/100 = 0.02$.

设原数字为 $x$，则向右移动小数点四位相当于将 $x$ 乘以 $10,000$。即 $10,000x = 4 \cdot (\frac{1}{x})$，这等价于 $x^2 = 4/10,000$。由于 $x$ 为正数，故 $x = 2/100 = 0.02$。

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