The Bohr Magneton is both a physical constant and the natural unit for expressing an electron magnetic dipole moment. The Bohr magneton (symbol: μB) is the magnitude of the magnetic dipole moment of an orbiting electron with an orbital angular momentum of one reduced Planck constant. This constant is expressed in electron volts per Tesla (eV/T).
This constant, the Bohr Magneton, μB, is specified with the standard uncertainty (standard deviation) of 0.0000000038 x 10-5 eV/T
See Uncertainty of Measurement Results, a discussion provided by NIST of the application of uncertainty to the documented constants.
Interested in the atomic model Neils Bohr created? See Socratia's video on the History of the Atom