Rounding to the nearest whole syringe unit is usually the right error to make, but understanding which direction it is and why matters.
Dead space quantified: a fixed-needle insulin syringe holds roughly 3 to 5 µL in the hub and needle after the plunger bottoms out. A luer-lock syringe with a detachable needle holds 35 to 100 µL depending on the hub design. At 5 mg/mL that is 15 to 25 µg lost per draw on the insulin syringe and 175 to 500 µg on the luer-lock — which over ten draws is the difference between losing a rounding error and losing half a milligram.
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.
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.
One qualification: if your arithmetic and someone else's disagree by a factor of ten, one of you has made a unit error, and writing out the units at every step is the diagnostic.
If in doubt, use more diluent and accept the shorter usable window.