Having done some research on bijective numeration - that is, a number system in which every non-negative integer can be represented in exactly one way using a finite string using a finite set of symbols - it occured to me that values "right of the radix", or values multiplied by a negative power of the base, a much trickier without the use of a zero.
If utilizing an empty string for zero, you couldn't rely on zeroes to indicate placement; that is, $0.001$ and $0.000001$ couldn't be distinctly displayed using the empty string, as both would appear as .1 (which is not all that helpful). Some potential solutions I pondered might be to have a marker, akin to the usage of a subscript number indicating what position the number is in. i.e., the aforementioned numbers could be $.1_3$ and $.1_6$ respectively. Another example being $37.109005$ represented as $37.1_19_35_6$. Alternatively, you could represent the numbers as fractions. So $1/k^3$, where k equals the base, and $1/k^6$. Both of these methods are potentially cumbersome, though.
However, fractions definitively cannot handle the case of irrational numbers, and given an irrational number won't terminate, it would be immensely cumbersome to denote the position of every single symbol less than 1, effectively doubling the symbols being written. Though, I suppose irrationals are already somewhat cumbersome. For some irrationals, I something like a continued fraction or series might be applicable, but I'm not sure about the closure of those methods regarding a bijective system. Even so, I was curious as to whether there was potentially an efficient manner of dealing with representing values with non-integer components in a bijective number system.