Problem:
Suppose that and are digits, not both nine and not both zero, and the repeating decimal is expressed as a fraction in lowest terms. How many different denominators are possible?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since , the denominator must be a factor of . The factors of 99 are , and 99 . Since and are not both nine, the denominator cannot be 1. By choosing and appropriately, we can make fractions with each of the other denominators.
Thus, the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions