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In the decimal representation of $\frac{1}{k}$, where $0 < \frac{1}{k} < 1$. the tenths digit is $1$, hundredths digit is $3$ and at least one other digit is nonzero. What is the tenths digit in the decimal representation of $\frac{k-1}{k}$

Please show me how the answer come up with "$8$" :(

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1 Answer 1

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Hint: $\dfrac{k-1}{k} = 1 - \dfrac{1}{k} = 1 - 0.13\ldots = $

Or, if we want to be more rigorous, $0.13 < \dfrac{1}{k} < 0.14$, so $1-0.14 < 1-\dfrac{1}{k} < 1-0.13$.

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