Suppose that a and b are digits, not both nine and not both zero, and the repeating decimal 0.abababab..... is expressed as a fraction in lowest terms. How many different denominators are possible?

toodlestraws Aug 3, 2020

#1**+1 **

x = .abababab....

100x = ab.ababab...

100x - x = 99x = ab

x = ab/99 ab can be 64 choices if they ab is 1 3 or 9 11 or 33 the denominator could be 99 33 or 11 9 or 3

so I THINK the answer is 5

ElectricPavlov Aug 3, 2020