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?
the largest possible value of x is just \(0.\overline{98}\). To convert that into a fraction:
\(100x = 98.\overline{98}\\ x=\overline{98}\\ 99x=98\\ x=\boxed{\frac{98}{99}}\)
