What can be the maximum number of digits in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ? Perform the division to check your answer.

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Solution

When $1$ is divided by $17$ , we get,
$\frac{1}{17} = 0. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0588235294117647$
So, the number of digit in the repeating block of digit in the decimal expansion of $\frac{1}{17} = 16$

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What can be the maximum number of digits in the repeating block of digits in the decimal expansion of 117? Perform the division to check your answer.

When 1 is divided by 17, we get,117=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0588235294117647So, the number of digit in the repeating block of digit in the decimal expansion of 117=16

What can be the maximum number of digits in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ? Perform the division to check your answer.

When $1$ is divided by $17$ , we get,
$\frac{1}{17} = 0. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0588235294117647$
So, the number of digit in the repeating block of digit in the decimal expansion of $\frac{1}{17} = 16$