The decimal representation of a fraction ends in $0.\overline{3}$. When the decimal is changed to a common fraction and reduced to lowest terms, what is the denominator of the fraction?
I notice that the decimal has a repeating digit of 3, so I can use a trick to convert it to a fraction. I let x be the decimal, so x = 0.\overline{3}. I multiply both sides by 10 to shift the decimal point one place to the right, so 10x = 3.\overline{3}. I subtract x from both sides to eliminate the repeating part, so 10x - x = 3.\overline{3} - 0.\overline{3}. I simplify the left side and the right side, so 9x = 3. I divide both sides by 9 to isolate x, so x = 3/9. I reduce the fraction to lowest terms by dividing the numerator and the denominator by 3, so x = 1/3. The denominator of the fraction is 3. 