Find the six-digit number abcdef such that

0.\overline{abcdef} = \frac{2}{17},

without a calculator.

BRAlNBOLT Jun 11, 2024

#1**0 **

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**.

Maxematics Jun 11, 2024