This is definitely not my area of expertise, but my understanding was that the mantissa was actually the source of inexactness in floats? I know the power bits

This is definitely not my area of expertise, but my understanding was that the mantissa was actually the source of inexactness in floats? I know the power bits (10 bits?) are pretty close to actual twos complement ints, and you could always do things in a C-like union, but I wasn't aware you could directly treat the mantissa like an int