In classical binary computers, real numbers are often represented using the IEEE 754 standard. With quantum computers you can of course do this as well - and for measurements this (or a similar standard) will probably be necessary since the result of any measurement is binary. But could real numbers be modeled more easily and / or more precisely within the qubits using different methods before the measurement happens? If so, are there any use cases where this is actually useful, seeing that (I'm assuming) any additional precision will be lost when measurements are performed?
To be clear, I'm not (necessarily) looking for existing standards, just for ideas or suggestions on how to represent those numbers. If there's any research into it, that would be useful too of course.