What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?
since, the number of entries in the repeating block of digits is less than the divisor. In $\frac{1}{17},$ the divisor is $17$.
$\therefore$ The maximum number of digits in the repeating block is $16 .$ To perform the long division, we have
The remainder $1$ is the same digit from which we started the division.
$\therefore$ $\frac{1}{17}=0 . \overline{0588235294117647}$
Thus, there are $16$ digits in the repeating block in the decimal expansion of $\frac{1}{17} .$ Hence, our answer is verified.
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