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 1

Find maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$.

Divide $1$ by $17$

$\frac{1}{17}=0.0\overline{588235294117647}$

There are $16$ digits in the repeating block of the decimal expansion of $\frac{1}{17}$.

The remainder never becomes zero and remainders repeat after a certain stage.

Thus, there are $16$ digits in the repeating block of the decimal expansion of $\frac{1}{17}$.