Uncertainty in number realization
Realization Uncertainty
There is a much more stronger fundamental limit to the precision of measurement for any analog value overpowering the effect of the Heisenberg's uncertainty principle. The uncertainty principle was derived from the fact that the complementary variables, such as position x and momentum p cannot be fixed simultaneously with higher precision. Instead of dealing with multiple variables, my observation is the limit to the precision of any single measurable analog value such as position x or angle a.
In fact, it is basically concerning about our human's incapability in realizing a irrational number such as 
For those who wander what realizing a number means, let me introduce one concept as follows.
I see two domains when I see a real number, one is ideal world and other is real world. And I see two domains need to be distinguished because a real number can be represented differently from each other domain. Mathematicians only care about the ideal domain for a real number but physicists care about only real part for it and it is obvious that there is a non-zero error in number representation when they convert it to the opposite domain.
Let's assume we want to prove something. In order to do that, we need to foretell something first and check it with the measurement later. One example is that I can predict that the sun will rise in the east tomorrow morning. In order to prove my prediction correct, then I need to wait till tomorrow morning and see if the sun rise in the east. the same process to prove something can be applied to the proof that for a number, representation in real domain is the sum of the representation in ideal domain Ni and non-zero error e. It should be noted that a famous irrational number 
Back to the uncertainty principle, I know position x can be any real number and it means it could be an irrational number. So for physicist preferring living in the real domain, it is somewhat meaningless to talk about precision limit of knowing the complementary variables simultaneously because it is obvious that there is a fundamental limit in realizing position x itself. At least for me, it will be suffice to consider my uncertainty principle solely to confirm that we can not predict what will happen. Again I want to note that what Heisenberg's uncertainty principle suggests is that predicting an object's whole movement is impossible without knowing position and momentum simultaneously.
