"Integer Float" Exact Conversion to Float

I am working with a library that uses int for representing money amounts. For example, the following is what this looks like:

599 --> $5.99
500 --> $5.00
5 --> $0.05
0 --> $0.00
-599 --> $-5.99

I wrote the following function which does an exact float conversion without causing floating point errors, but what I am wondering is if I am approaching this the wrong way or if there is a much cleaner solution.

def money_int_to_float(value: int) -> float:
    neg: str = '-' if value < 0 else ''
    value = abs(value)

    cents: int = value % 100
    remaining: int = value - cents
    dollars: int = int(str(remaining).removesuffix('00'))
    return float(f'{neg}{dollars}.{str(cents).zfill(2)}')

My reasoning for wanting an exact float conversion is that when dealing with money you can never be too careful with floats.

source https://stackoverflow.com/questions/73365148/integer-float-exact-conversion-to-float