Ternary Expansion of x ∈ [0,1] - Tips & Tricks

[jakey]

Hi guys, I'd like to ask about ternary expansions. they seem easy but I'm having a hard time doing this as well as searching for tips online, specifically for x \in [0,1].

I know that ternary expansions are similar to decimal expansions but for example, how do you find the ternary expansion of \frac{5}{3^3} ?

 

[HallsofIvy]

In base 3, 5= 3+2 is 12_5. Of course, 9= 3^2 is 200_3 so the fraction 5/9, in base 3, would be the fraction 12/200. Can you write that in "trinary"?

 

[jakey]

Hi hallsofivy, sorry I didnt quite understand your reply.

And oh, it's 5/27 not 5/9. Perhaps a better way of explaining it to me would be how to identify the coefficients a_k such that \frac{5}{27} = \sum \frac{a_k}{3^k} ?