1996 AJHSME Problems/Problem 11
Problem
Let be the number where there are 1996 zeros after the decimal point. Which of the following expressions represents the largest number?
Solution
Estimate each of the options.
will give a number that is just over .
will give a number that is just under . This eliminates , because is bigger.
will give a number that is barely over , 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 , which gives as the reciprocal, , which gives as the reciprocal, and , which gives 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.
See Also
1996 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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