What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.
Question
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ? Perform the division to check your answer.
Answer
The decimal expansion of $\frac{1}{17}$ is $0.\overline{0588235294117647}$, where the repeating block of digits in the decimal expansion is "0588235294117647". Therefore, the maximum number of digits in the repeating block is 16.
This shows that when dividing by 17, the repeating block of the decimal expansion can have up to 16 digits.
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