Actually there's no limit, just like we are changing reference frames on Earth to keep a good precision with floating point values, we can change the reference frames in space to have both good precision and covering a huge space.
But let's say that without changing the reference frame, and keeping 0.001m precision everywhere, we can get to ±2,251,799,814 kilometers from Earth. After that the precision will start getting worse, like 0.002m for another 2,251,799,814 kilometers and so on.