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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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.
Problem 33 in Other Years
1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12 · 1968 AMC 12 · 1969 AMC 12 · 1970 AMC 12 · 1971 AMC 12 · 1972 AMC 12 · 1973 AMC 12