Taking the question as asked, rather than the general version of it. 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.

PurityPaulOR said:

Do it in two steps and it stops being confusing.

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.

TirzTom 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. 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.

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

Just received my dosing arithmetic order — packaging review:

• Outer box: plain brown, no medication identifiers (discreet) ✅
• Inner insulation: Styrofoam with 4 gel ice packs ✅
• Temperature: vials were cold to touch on arrival ✅
• Labeling: lot number, BUD, compound name, concentration ✅
• Included: COA, reconstitution instructions, dosing card ✅

This is what professional compounding pharmacy shipping looks like. If your order arrives without these basics, reconsider your vendor.