The single most useful thing to do is write the arithmetic on the vial label, because you will reconstruct it from memory at an inconvenient moment if you do not.
Worked example, because the general form is easier to trust once you have seen it once. Take a 10 mg vial and add 2 mL of diluent: the concentration is 10 ÷ 2 = 5 mg/mL. A 0.5 mg dose is 0.5 ÷ 5 = 0.1 mL. On a U-100 syringe, where 1 unit = 0.01 mL, that is 0.1 ÷ 0.01 = 10 units. Change the diluent to 1 mL and the same dose becomes 5 units — same dose, half the resolution.
On the detail: 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.
Published data on syringe dead space quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more for conventional detachable-needle syringes.
Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.