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Suppose that a and b are digits, not both nine and not both zero, and the repeating decimal x = 0.abababab..... is expressed as a fraction in lowest terms.  What is the largest possible value of x?

 Feb 4, 2021
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the largest possible value of x is just \(0.\overline{98}\). To convert that into a fraction:

\(100x = 98.\overline{98}\\ x=\overline{98}\\ 99x=98\\ x=\boxed{\frac{98}{99}}\)

 Feb 5, 2021

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