It helps to be literal here: dose arithmetic has three parts: concentration from vial content and diluent, volume from dose and concentration, and units from volume and syringe scale.
Dead space quantified: a fixed-needle insulin syringe holds roughly 3 to 5 µL in the hub and needle after the plunger bottoms out. A luer-lock syringe with a detachable needle holds 35 to 100 µL depending on the hub design. At 5 mg/mL that is 15 to 25 µg lost per draw on the insulin syringe and 175 to 500 µg on the luer-lock — which over ten draws is the difference between losing a rounding error and losing half a milligram.
Rotation of injection site is a tolerability measure, not a pharmacokinetic one, but if you are going to do it you might as well do it right.
I would flag the obvious failure mode: people get the concentration right, get the volume right, and then read the syringe against the wrong scale.
Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.
edited 28 Aug 2025 by orla_ferriter — added the method parameters