Converting base 10 fractions into other bases 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 $112.\overline{121}_{3}$

Just like you convert a fraction to decimal.  $8\cdot 3=24=13(1)+11,$ so the first digit (ternit?) is $1. \ \  11\cdot 3=33=13(2)+7,$ so the second digit is $2. \ \  3\cdot 7=21=13(1)+8$ and so on.  I get $112.\overline{121}_{3}$
Alternately you can notice that $\frac{8}{13}=\frac{16}{3^3-1}$, so the repeat is $3$ digits long and is $16_{10}=121_3$
