Ok if we are both in freefall (for example in the space shuttle) it would still follow newtonian mechanics, at least to within the limits of what can be measured by practical means.
In general things can not be measured to infinite precision as in your example. In some parts of particle physics you can get to 14 or 15 digits, but in other cases (for example distances to stars) you are happy if you can get to within 10%. In the case of gravity we only know the value of the gravitational constant to about 4 decimal places. (And that took a few hundred years to do)
And while there is always a difference between classical and relativity or Quantum physics it is often so small you can ignore it, as it will be smaller than other effects. Of course a large part of a physics degree is knowing when that is.