Conversion factor for chemical to physical scale of atomic masses Before the 1960s chemists and physicists used to have different atomic mass tables. The main difference was that the physicists assigned the $^{16}$O as the O=16 from mass spectrometry. Chemists on the other hand were using the ordinary oxygen which is a mixture of $^{16}$O, $^{17}$O and $^{18}$O as O=16. Of course, this confused everyone before carbon-12 was suggested as a compromise as both parties were not willing to budge. The % abundance of $^{16}$O is 99.76, $^{17}$O is 0.04, $^{18}$O is 0.2.

People were able to develop a conversion factor between a chemist's atomic mass and a physicist's atomic mass tables. A book by Guggenheim "Physicochemical Calculations" shows the example how the conversion factor was obtained. He doesn't explain anything clearly.

Could anyone shed some light, how the author is calculating this factor? I assume by $$\frac{O}{^{16}O}$$ the author mean how heavy is ordinary oxygen with respect to true $^{16}$O . I don't know where 1 is coming from and why there is a 2 besides O-18 isotope.
$$\frac{\ce{O}}{\ce{^16O}}=\frac{(.9976\times\ce{^16O})+(.0004\times\ce{^17O})+(.002\times\ce{^18O})}{\ce{^16O}}$$
$$=\frac{(.9976\times\ce{^16O})+(.0004\times(\ce{^16O}+1))+(.002\times(\ce{^16O}+2))}{\ce{^16O}}$$
$$=\frac{(\ce{^16O})+(.0004\times1)+(.002\times2)}{\ce{^16O}}$$

Essentially, it comes from collecting factors of $\ce{^16O}$.