Balanced based representation I'm interested in balanced base $B$ representation for fixed point arithmetic. The paper Fixed-point arithmetic in SHE schemes (Costache, Smart, Vivek and Waller, in Proceedings of 23rd International Conference on Selected Areas in Cryptography (SAC 2016), Springer Lecture Notes in Computer Science, vol.&nbsp;10532, pp.&nbsp;401&ndash;422, 2016; PDF) provides two examples using balanced based $B=3$. However, I don't understand the 2nd second representation, i.e. 
$$\frac{8}{3}=10.\bar{1} $$
where $\bar{1}=-1$. 
More generally speaking, I'm also interested in balanced form representation $B=5, 7$.
I believe this should be a well-known problem, though I was not able to google it. Do you know some relevant literature to this?
The expression $10.\overline{1}$ should be interpreted as follows:
$$
1 \cdot 3^1 + 0 \cdot 3^0 + (-1) \cdot 3^{-1} = 3 - \frac{1}{3} = \frac{8}{3}.
$$
The interpretation of balanced base $b=2d+1$ is the same, with the digits ranging from $-d$ to $d$.