MathDB
Repeating Decimal

Source:

April 6, 2008

Problem Statement

Suppose that a a and b b are digits, not both nine and not both zero, and the repeating decimal 0.ab 0.\overline{ab} is expressed as a fraction in lowest terms. How many different denominators are possible? <spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 5 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 9