zoe_NC said:

Concentration choice is a precision decision, not a preference.

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

zoe_NC said:

Concentration choice is a precision decision, not a preference.

I am going to disagree with reconstituting low as a general rule. More diluent, more punctures, more in-use days at room temperature, and the stability trade-off is real. Precision is not the only variable being optimised.

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.

julia.endo said:

Dead space is the answer to the missing dose.

This matches mine closely enough to be worth saying so out loud.