This is one of those calculations where checking your work takes two minutes and prevents a very consequential error.
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 content assay results from major testing services show that nominal vial claim and measured content differ by one to ten per cent, making content a driver of dose error.
I would flag the obvious failure mode: people get the concentration right, get the volume right, and then read the syringe against the wrong scale.
Do the arithmetic twice, ideally with someone else doing it independently.