Accuracy of known constants versus precision I am wondering if the community could comment on the accuracy of the known constants versus their precision.  What I mean is while many values like the electron magnetic moment are known to extraordinary precision ~12 decimal places, what do we know about the accuracy of the reported values?  Especially when one considers that there are empirical constants such as the gravitational constant $G$ for which there is no theory which can relate said constant to others, it seems like there is potential hole(s) in our understanding which might suggest any theory that could relate an empirical constant to other known ones with high precision might require a fundamental re-alignment of those other constants to be consistent.
 A: First, it's important to note that some of the constants of nature are "infinitely accurate" by definition because we have defined our system of units so that these constants are exact integers.  The meter is defined to be the distance travelled by light in vacuum in 1/299,792,458 of a second (exactly);  this means that the speed of light is exactly 299,792,458 m/s.  Similarly, the kilogram is defined to be the unit of mass so that Planck's constant is exactly equal to $6.62607015 \times 10^{−34} \text{ kg}\cdot\text{m}^2/\text{s}$.  The fundamental unit of charge and Boltzmann's constant are also exact numbers because of how we have defined the units of charge and temperature in the SI system.
This does leave several other constants of nature that just have to be measured, such as the gravitational constant, the mass of the electron, various neutrino mixing angles, etc.  It is conceivable that a theoretical model could predict that (for example) the gravitational constant $G$ times the electron mass $m_e$ should be some exact integer fraction of the speed of light squared.  If so, then we would need to look at the error bars on the measurements of $G$ and $m_e$ and see if the measured values are consistent with this prediction.  If they are not, then the theoretical model would be wrong and we would have to discard it.
