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.

Dr.BariatricHTX said:

Dead space is the answer to the missing dose.

No disagreement with Dr.BariatricHTX. One condition attached. 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.

Dr.RenalNash 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.

Peptide calculator app recommendation for dosing arithmetic: I use DoseRight to calculate reconstitution volumes and injection doses. Eliminates math errors completely.

Input: vial size (mg), desired concentration (mg/mL), prescribed dose (mg)
Output: BAC water volume (mL), injection volume (units on insulin syringe)

A math error with injectable medication can mean underdosing or overdosing. Use a calculator every time until the math becomes second nature.