can we measure that imprecision of momentum/position relation even though small?
For example, here's an object of 1 kg mass. The product of the uncertainty of its position and momentum is h-bar / 2, or h / 4 pi, which is about 5e-35 kg m^2/s. We're going to measure the position to one wavelength of visible light (say, 500 nm wavelength, so 5e-7 m). That means that we need to be able to measure the momentum to an accuracy of 1e-28 kg m/s, which for a mass of 1 kg means measuring the velocity to within an accuracy of 1e-28 m/s. Good luck with that...
You can in theory but the numbers get so small that they're clearly unmeasurable.