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10

Part of 2014-2015 SDML (Middle School)

Problems(1)

Repeating decimal denominator

Source: 2014-2015 SDML Middle School 1a Problem 10

8/28/2016
Suppose aa and bb are digits which are not both nine and not both zero. If the repeating decimal .AB‾.\overline{AB} is expressed as a fraction in lowest terms, how many possible denominators are there?
(A) 2(B) 3(C) 4(D) 5(E) 6\text{(A) }2\qquad\text{(B) }3\qquad\text{(C) }4\qquad\text{(D) }5\qquad\text{(E) }6