Q.5. 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.

Solution:

The maximum number of digits in the repeating block of digits in the decimal expansion of $\frac{1}{\mathrm{n}}$ can be (n-1). Therefore, the maximum number of digits in the repeating block of the decimal expansion of $\frac{1}{17}$ can be 16.

This can be verified by long division method, and we get,

$\frac{1}{17}$ = 0.0588235294117647 (16 digits).