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# repeating decimal

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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

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