How do you convert
$14\frac{8}{13}$
into base 3?
I was able to convert $\frac{3}{7}$ into base 3 by constantly multiplying by 3 and dividing the numerator by denominator until I finally got a repetition, but this method doesn't seem to work for $14\frac{8}{13}$.
The correct answer is supposed to be $112.\overline{121}_{3}$