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Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{2}{17},
without a calculator.

 
 Jun 11, 2024
 #1
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For a number to be written as \(0.\overline{abcdef}\), you must be able to write it as \(\frac{abcdef}{999999}\). Therfore, we can just divide 999999 by 17 to find the factor we need to multiply 2/17 by. Using a bit of scrap paper, we find that 999999 / 17 is not a whole number (it's aapproximately 58823.471). Therefore, it is impossible to make a 6-digit number that has that property.

 Jun 11, 2024

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