I am seeing two different formulas for the mixing ratio, which differ by a factor 1000. To be more specific:
$w = 0.622 \cdot (e/p)$
$w = 1000 \cdot 0.622 \cdot (e/p)$
where $e$ and $p$ are the water vapour pressure and the atmospheric pressure, respectively.
I assume the factor 1000 has to do with the fact that the mixing ratio is theoretically a ratio of masses, so probably the numerator can be expressed in grams and has to be converted to kilograms, but I'm confused because I don't see masses in these formulas.
What's the difference between the two ?