Stated carefully, the single most useful thing to do is write the arithmetic on the vial label, because you will reconstruct it from memory at an inconvenient moment if you do not.
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.
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 Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.
The caveat is that this assumes the vial contains what the label says, and if the content assay has not been done, the arithmetic is precise about an unknown quantity.
Do the arithmetic twice, ideally with someone else doing it independently.