Accepted answer
At 2.5 mg/mL every microlitre left behind is 2.5 µg, so a 50 µL hub costs 0.125 mg per draw and a 5 µL fixed-needle barrel costs 0.0125 mg. Multiply by the draws, not by the doses: ten draws through a 50 µL dead space is 1.25 mg gone, which at 2.5 mg/mL is 0.5 mL of solution you paid for and never administered. Against a 2 mg dose that 50 µL is 6.3 per cent; against a 0.25 mg dose it is 50 per cent, which is why the loss matters most at exactly the doses where you can least afford it. a 31G needle has a bore, a hub and a length, and the hub dominates: a fixed-needle insulin barrel has almost none, a luer connection has a measurable one before the needle even starts.
Dead space is the volume trapped in the syringe hub and needle after the plunger bottoms out, and it is the reason your 10 mg vial yields only 9.5 mg of usable draws.
Be sceptical of anything advertised as low dead space that retains a conventional plunger tip: if you can look into the fitting with the plunger fully forward and see an open conical void, that void is your dead space.
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.
Syringe residual volume has been measured properly, mainly in the infection-control literature, with a median residual of about 84 µL for a conventional 1 mL syringe with a detachable needle and roughly 2 µL for a fixed-needle low-dead-space design.
Buy the right syringe — a fixed-needle insulin syringe is cheap and solves the problem.