1989 AMC 8 第 18 题
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18.
计算器上有一个倒数键，按下它会把当前显示的数换成它的倒数。例如，若显示屏上是 ，按一次该键后显示 。如果显示屏上是 ，至少按几次倒数键才能再次显示 ？
A calculator has a reciprocal key that replaces the number currently displayed with its reciprocal. For example, if the display shows and the key is pressed, the display becomes If is currently displayed, what is the fewest number of times the reciprocal key must be pressed so that the display again reads
小提示：
按一次会把 变成它的倒数 。
Pressing the key once turns into
大提示：
一个数的倒数再取倒数，会回到原来的数
The reciprocal of the reciprocal of a number is the number itself
解答：
从 开始，按一次倒数键会得到 。
再按一次，就是对倒数再取倒数，得到 。所以最少需要按 次。
所以正确答案是 B。
Pressing the key once changes to its reciprocal
Pressing it a second time takes the reciprocal again, returning to So presses are enough.
Thus, the correct answer is B .
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