i agree with the comment two comments above mine. fractional bases using the exploding dots method would be great.
here are some more numbers to make it clear what's going on if you don't get it:
4 in base 1 1/3: 30
6 in base 1 1/5: 50
4 in base -1 1/2: 211 (actually this one's probably gonna be a bit hard to calculate tbh)
11 in base 1 1/10: A0
if we convert these fractions into improper fractions (4/3, 6/5, -3/2, 11/10), we can see that the number in the numerator is the first double-digit number, with an amount of tens equal to the denominator.
you could program an exploding dots system kinda like so:
given a number, take [numerator] out of said number, and for each time that's done, add [denominator] to the left of it. repeat this process with the digit to the left until the number only uses digits between 0 and [numerator - 1]. the rules may change with bijectives and balanced bases and whatnot, but this is how it is with positive fractional bases.
*before moving on to the digit to the left, repeatedly subtract [numerator] to the digit and add [denominator] to the left of it. i forgot to clarify that this is a process to be repeated (or you could find a faster way than performing a process repeatedly)
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