Short answer first, then the reasoning. 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.

TirzTom said:

Dead space is the answer to the missing dose.

Agreeing with TirzTom, and the qualification matters more than the agreement. 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.

patPC_UT said:

Two of us with identical vials and identical diluent arrived at different unit counts, which means one of us has a conceptual error rather than a…

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.

From the other side of the consultation, briefly.

For anyone reconstituting dosing arithmetic peptides: the water-to-powder ratio determines your concentration. Here's my reference:

More water = easier to measure small doses but vial runs out faster. Find the balance that works for your dose.