I taught chemistry for 30 years and never encountered the unit until I saw it on a juice bottle!
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3$\begingroup$ Using "u", "amu" or "Da" is mostly a matter of taste. In chemistry, I'd stick to SI and use g/mol. Biochemists love Daltons, I don't know why. $\endgroup$– KarlNov 13, 2016 at 13:27
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5$\begingroup$ @Karl $\mathrm{g/mol} \ne \mathrm{Da}$. $\endgroup$– JanNov 13, 2016 at 15:48
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The atomic mass unit (amu) was not renamed to dalton (Da). These are different, albeit related, units.
The atomic mass unit (amu) referred to the relative atomic mass of oxygen, which was taken as 16. However, physicists used the atomic mass of the nuclide $\ce{^16O}$ whereas chemists used the average atomic mass of natural oxygen. This unit became obsolete when IUPAP (1960), IUPAC (1961), ISO, CIPM (1967) and CGPM (1971) agreed to assign the value 12 to the relative atomic mass of the nuclide $\ce{^12C}$.
The unit dalton (Da) and the unified atomic mass unit (u) are non-SI units that are accepted for use with the SI. Actually, ‘dalton’ and ‘unified atomic mass unit’ are alternative names for the same unit, equal to 1/12 times the mass of a free carbon-12 atom, at rest and in its ground state, i.e.
$$1\ \mathrm{Da} = 1\ \mathrm{u} = 1.660\,538\,921(73) \times 10^{-27}\ \mathrm{kg}$$
Therefore, using the old definition of the atomic mass unit (amu) in physics
$$1\ \mathrm{Da} = 1\ \mathrm{u} \approx 1.0003\ \mathrm{amu}$$
and using the old definition of the atomic mass unit (amu) in chemistry
$$1\ \mathrm{Da} = 1\ \mathrm{u} \approx 1.00006\ \mathrm{amu}$$