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.
Room temperature before drawing is worth the ten minutes. Cold solution is more viscous, draws slower, and condensation on a cold barrel makes it harder to read the meniscus.
Worth noting: the concentration after reconstitution is not the same as the label claim, and most people do not account for the difference.
Do the arithmetic twice, ideally with someone else doing it independently.
edited 10 Dec 2024 by h_pergande — reworded for clarity after a comment