1956 AMC 12 Problem 33
Attempt Problem 33 of the 1956 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1956 AMC 12 solutions, or check the answer key.
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33.
The number is equal to:
a rational fraction
a finite decimal
an infinite repeating decimal
an infinite non-repeating decimal
Answer: E
Small hint:
Recall what kind of decimal expansion every rational number has
Big hint:
The number is irrational, so its decimal neither terminates nor repeats
Solution:
The number is irrational. A rational number has a decimal expansion that either terminates or eventually repeats, whereas an irrational number has an infinite non-repeating decimal expansion. The finite decimal is only an approximation.
Thus, the correct answer is E.