Question

Question 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.

Answer 1

$\frac{1}{17}=0.\overline{0588235294117647}$

Division Check:
$\stackrel{0.0588235294117647}{17\sqrt{100}}$
$-85\overline{}150-136\overline{}140-136\overline{}40-34\overline{}60-51\overline{}90-85\overline{}50-34\overline{}160-153\overline{}70-68\overline{}20-17\overline{}30-17\overline{}130-119\overline{}110-102\overline{}80-68\overline{}120\overline{}=0.0588235294117647$
There are 16 digits in the repeating block of the decimal expansion of $\frac{1}{17}$.