I pulled out my copy of Knuth vol 2 to answer this (pages 190-193):
* You can negate a number by interchanging 1 and ̅1.
* The sign of a number is given by its most significant non-zero trit.
* Rounding to nearest integer is the same as truncation.
By the way if we had balanced ternary computers today, then you wouldn't have programming languages with signed and unsigned integers. They'd be the same thing.
Of course the above might be academic if it's more difficult to implement in CMOS ...
Edit: Also you can argue that the most economical radix is e, and 3 is closest to this ideal. See: https://web.williams.edu/Mathematics/sjmiller/public_html/10...
Edit #2: Removed the claim that addition is easier than binary. I misread what Knuth was trying to say.