Answering the narrow version, because the broad one does not have a single answer. 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.

Dr.ObesityLA said:

Do it in two steps and it stops being confusing.

Dr.ObesityLA has the substance of this right. The condition it depends on is worth stating. 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.

nick_newbie said:

I reconstituted a 10mg vial with 2ml of bacteriostatic water and I want someone to check my unit arithmetic before I draw anything, because I keep…

This matches mine closely enough to be worth saying so. Concentration choice is a precision decision, not a preference. Reconstitute high and every dose is a tiny volume where one unit of syringe error is a large fraction of the dose. Reconstitute low and you get more graduations per dose, so the same hand tremor costs proportionally less. Against that, more diluent means more benzyl alcohol and a shorter comfortable in-use window.

Clinical perspective, offered as context rather than as advice.

Regarding dosing arithmetic multi-dose vial contamination prevention: after reconstituting, I wipe the vial stopper with a fresh alcohol swab before EVERY single draw. I also never touch the stopper with my fingers and use a new needle for each draw.

Even with bacteriostatic water preservative, contamination is cumulative. One sloppy draw can introduce bacteria that multiply over days. Aseptic technique isn't optional — it's essential for injectable medications.