Quantum Physics and Pure Numbers

There is a very natural relationship between numbers and quantum physics. In practice can only write a number down to so many significant figures. IN practice you only calculate a physics quantity to so many significant figures.. In the case of numbers this is true even for those numbers like
, and in the case of quantum mechanics, even for those quantities that are the exact solutions too some exact equation, like the metafunction of an electron inside a quadratic potential well.
In fact no physical equation can be exact, because the coefficients, which are in terms of some physical quantity such as mass or spring constants, are not exact, so the solutions to the equation are subject to a limit on accuracy approximately equal to the number of significant figures to which the coefficients accurate.
Suppose then that all the numbers representing constants in the equations were truncated to a fixed number of significant figures. Then all the numbers representing the variables would also be uncertain to a related number off significant figures.

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