TITLE: How to convert a fraction into ternary?
QUESTION [16 upvotes]: In a ternary system how is $\dfrac{1}{2}=0.\bar1$ ,$\dfrac{1}{3}=0.1=0.0\bar2$??, etc. In general, how does one write the ternary expression for a given fraction?

REPLY [9 votes]: The easiest way to do it, I think, is to convert everything before the decimal point the regular way. Then you just repeat the following process:

Subtract 1 until you get between 0 and 1.
Multiply by 3.
The integer part of your answer is the next digit of the ternary expansion.
Rinse and repeat.

Example, using $\frac{15}{4}$:
The integer part is 3, so we write $10_3$. We're now left with $\frac{3}{4}$. Multiply by 3 to get $\frac{9}{4}$, having an integer part of 2. So we have $10.2_3$. Subtract the 2 from the $\frac{9}{4}$, and we have $\frac{1}{4}$. Multiply by 3, we get $\frac{3}{4}$. This has no integer part, so the current result is $10.20_3$. Now, this will repeat, as is obvious, so the end result is $10.\overline{20}_3$.
Now, as to why this works, it is just a visualizing of trying to express the decimal part by fractions with denominator a power of 3. Which is what ternary decimal expansion is.
Edit: I realize that this answer is pretty darn equal to Mike Spivey's, and mine is much less precise and stuff. Sorry about that.