In real life, no instrument is going to give you a measurement with the 52 bits of precision a double can offer, and you are probably never going to get quantities are in the 10^1000 range. No actuator is precise enough either. Even single precision is usually above what physical devices can work with. When drawing a pixel on screen, you don't need to know its position down to the subatomic level.
For these real life situations, improving on the usual IEEE 754 arithmetic would probably be better served with interval arithmetic. It would fail at maths, but in exchange you get support for measurement errors.
Of course, in a calculator, precision is important because you don't know if the user is working with real life quantities or is doing abstract maths.