Accepted answer
This is arithmetic, so let us do the arithmetic rather than argue about it.
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: the concentration you actually work with is label claim times content fraction divided by actual diluent volume, which is usually not the same as the nominal concentration because content is usually not 100 per cent and you rarely measure the diluent volume to 0.1 mL precision.
The Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.
Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.
edited 30 Aug 2024 by leonid_marchuk — added the placebo-arm figures