Can we think of a hypothetical experiment to determine the exact position of an object? Here is an extract from the book "The Elegant Universe"- "When we bounce a wave off of an object, the information we receive is only enough to determine object's position to within a margin of error equal to the wave's wavelength".
I was wondering why this is so? Can we imagine to set up an experiment in the laboratory to determine the exact position of an object by sending a beam of light? 
 A: This is because of quantum mechanics. The electron has a wave function which will not be perfectly localized at a position. From the wave function we get a probability distribution of it's position and since the wave function was not perfectly localized the electron will have a non zero probability of being at more than one position at any time.  This is what Brian Greene means when he talks about wavelength. If you try to be precise in determining exact position of electron you begin to "see" its "wave" nature. But its wave nature necessarily entails the fact that the electron is not perfectly localized in position.
A: Yes, obviously you can determine the exact position of an electron (disregarding the experimental errors) says the uncertainty principle. But since they (momentum and position) don't commute hence you totally lose the information of momentum about the electron!
Summary: Know the exact position and you lose momentum, know the exact momentum you lose the information about the position!! 
Also if the system is in an eigenstate then the uncertainty is lost! 
