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jmc

number theory junior

Problem

One digit of the decimal representation of is randomly selected. What is the probability that the digit is a 4? Express your answer as a common fraction.
Solution
The decimal representation of is , which has a repeating block of 6 digits. Since 4 is one of those six digits that keep repeating, the probability that the selected digit is a 4 is .
Final answer
\frac{1}{6}