Answering the narrow version, because the broad one does not have a single answer. Dead space is the answer to the missing dose. A fixed-needle insulin syringe holds a few microlitres in the hub and needle after the plunger bottoms out, and on small draws that is a measurable percentage of every dose. Across ten draws it adds up to most of an eleventh, which is exactly the "nine draws from a ten-dose vial" complaint. Luer-lock syringes are worse; low-dead-space fixed-needle designs are better.

Happy to go further on any of that.

DataDave said:

Dead space is the answer to the missing dose.

Agreed, and it is worth saying that rounding to the nearest whole unit is usually acceptable at maintenance doses and is not acceptable at the bottom of a ladder, where one unit can be a fifth of the intended dose.

DadBodDave 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…

Same position here, arrived at the long way round. 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.

Adding the clinical framing, because it changes how the question reads.

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.