How do you convert the μmol/mol units for atmospheric CO2 into CO2 mass fraction?

Question

The Keeling curve reports CO₂ in units of μmol/mol, but people's (and country's) emissions are generally reported in kilograms or tons of CO₂. I would like to convert μmol/mol of CO₂ in the atmosphere to mass fraction of CO₂ in the atmosphere using an accurate, well-established, and scientifically accepted method to ensure that my calculations are reproducible by others. What is the preferred way to do this?

Answer 1

TL;DR: Multiply $\ce{CO_2}$ expressed in μmol/mol by 1.52 the μg/g equivalent.

Details: The molecular mass of $\ce{CO_2}$ is 44.01 g/mol. The standard molecular mass of dry air is 28.9647 g/mol. Multiplying $\ce{CO_2}$ expressed in μmol/mol by 44.01/28.9647=1.5194 comes rather close. A tricky detail is that some of that standard molecular mass of dry air includes a small contribution from $\ce{CO_2}$. After accounting for this I get a value close a bit over 1.5196. Rounding either value to three significant digits results in a conversion factor of 1.52.