What can the maximum number of digits be in t | vedclass

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(A) In the decimal expansion of a rational number $\frac{p}{q}$,the number of entries in the repeating block of digits is always less than the divisor

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) In the decimal expansion of a rational number $\frac{p}{q}$,the number of entries in the repeating block of digits is always less than the divisor $q$.In the fraction $\frac{1}{17}$,the divisor is $17$.Therefore,the maximum number of digits in the repeating block is $17 - 1 = 16$.By performing long division,we find:$\frac{1}{17} = 0.\overline{0588235294117647}$Thus,there are $16$ digits in the repeating block of 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 $\frac{1}{17}$?

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