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When expanded as a decimal, the fraction $\frac{1}{7}$ has a repetend (the repeating part of the decimal) of $142857$.  The last three digits of the repetend are $857$.

 

  When expanded as a decimal, the fraction $\frac{1}{13}$ has a repetend that is $6$ digits long.  If the last three digits of the repetend are $ABC$, compute the digits $A$, $B$, and $C$.

 Oct 15, 2024
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Try to do long division with \(1 \div 13\). If you do that you should get that \(\frac{1}{13} = 0.\overline{076923}\)

 

Therefore, \(\mathbf{(A, B, C) = (9, 2, 3)}\)

 Oct 17, 2024

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