I'm not sure, but I suspect your best alternative to 32-bit floats/floating-bar-rationals or 64-bit rationals when you have no FPU is a 64-bit fixed-point value

I'm not sure, but I suspect your best alternative to 32-bit floats/floating-bar-rationals or 64-bit rationals when you have no FPU is a 64-bit fixed-point value with compressed floating-point representations if you need to store it compactly in memory.