To be exact about it, the distinction that resolves most of these questions is understanding what concentration actually means and why it is not the same as label claim.
The rounding error accumulates if you round too many times — rounding concentration to 5.0, rounding the dose volume to 0.1 mL, rounding the unit reading to 10 — and the safest approach is to work the full precision and round only the final answer.
Do not use the same needle to pierce the stopper and to administer. The tip is blunted by the stopper, and the hub now contains a dose you are about to lose to dead space anyway.
The insulin-unit standard U-100 means 100 units per millilitre, so one unit is 0.01 mL — this is the conversion that trips up more people here than any other single piece of arithmetic.
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.