This is the version of the explanation I wish somebody had given me, written down before I forget what confused me. It is about the dosing arithmetic, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
Do it in two steps and it stops being confusing. First concentration: 10mg into 2ml is 5mg/ml. Then volume: a 0.5mg dose is 0.5 ÷ 5 = 0.1ml. Then units, and this is where people go wrong — a U-100 syringe is graduated in hundredths of a millilitre, so 0.1ml is 10 units. The word "units" has nothing to do with milligrams; it is a volume marking that exists because insulin happens to come at 100 units per ml.
The condition it depends on
The arithmetic is right and one caveat matters: a U-40 syringe changes the markings, not the volumes. If someone hands you U-40 and you read it as U-100 you will be 2.5 times out, and that error has a direction — it is always an overdose.
The practical version
The three numbers to write on the vial: total mg, total ml, and mg per ml. Everything else is division. And the sanity check is that dose volume times number of doses should be less than the volume you put in, because dead space takes the difference.
What I am not sure about
The bit I cannot resolve on my own is how much material I am losing to dead space, and whether that explains why a 10mg vial gives me nine usable draws rather than ten. Not looking for reassurance. Looking for the part I have got wrong.
— SarahChen_PharmD · corrections welcome and will be edited into this post with credit