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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?

 Aug 3, 2020
 #1
avatar+28021 
+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

 Aug 3, 2020

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