Accepted answer
25 units is 0.25 mL, which at 1 mg/mL is 0.25 mg. Work it in that order and there is nothing to guess at: units to volume on the U-100 scale, volume to dose through the concentration. Draw with the barrel vertical, expel the air before you read, and read the leading edge of the plunger stopper rather than the shoulder — the difference between the two is about a unit on a 0.3 mL barrel.
The relevant precision limit is that you cannot reliably read half a graduation, so the barrel decides the smallest change you can make.
The conversion in full: volume in mL = dose in mg ÷ concentration in mg/mL; units = volume × 100. At 5 mg/mL, a 0.25 mg dose is 0.05 mL, which is 5 units. At the same concentration a 1 mg dose is 0.2 mL, which is 20 units.
Read the leading edge of the rubber plunger stopper against the graduation, not the tip of the conical shoulder. The difference is roughly one unit on a 0.3 mL barrel, which is a four per cent error on a 25-unit dose.
U-100 is a concentration standard meaning 100 units of insulin per millilitre; the syringe graduation is a volume scale expressed in those units.
One unit is 0.01 mL on U-100. That is the whole scale.