No—you can have arbitrarily many decimal places. Each time a coin splits in two, you could add another binary digit. But I don’t think this has to be limited to dividing coin denominations by two each time, the way it is in One proposal for plasma cash with coin splitting and merging. You can define arbitrary denominations at the time of splitting. If someone tries to lie about a coin denomination when they’re withdrawing, anyone who has the actual split in their history is able and incentivized to challenge it by revealing the actual split.
This does probably mean that you can’t merge two adjacent coins to get one coin with the ID of the pre-split parent, because that would allow coins to be resplit with different denominations, potentially causing a lot of confusion. But I’m sort of skeptical you’ll really be able to reverse coin-splitting entropy that often. And I think the method I describe above for merging is adequate as well as much more general.