AMC 8 1996 Problem 11
AMC8 1996 年第 11 题
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Let be the number
where there are 1996 zeros after the decimal point. Which of the following expressions represents the largest number?
设 为上面所示的数（小数点后有 1996 个零）。以下哪个表达式表示最大的数？
- A.3+x
- B.3-x
- C.
- D.3/x
- E.x/3
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Estimate each of the options.
will give a number that is just over 3.
will give a number that is just under 3. This eliminates , because is bigger.
will give a number that is barely over 0, since it is three times a tiny number. This eliminates , because is bigger.
will give a huge number. will get very, very large in magnitude when 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, will be huge, and this eliminates .
will give a small number, since you're dividing a tiny number into thirds. This eliminates , and gives as the answer.
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