Accepted answer
8 ÷ 0.5 = 16 mg/mL. Concentration is vial content divided by diluent volume, so 8 mg of peptide in 0.5 mL of sterile water for injection gives 16 mg/mL. On a U-100 barrel one unit is 0.01 mL, so one unit of this solution carries 0.16 mg — 160 µg. That is the number to write on the label, because you will not reconstruct it from memory at an awkward moment.
The distinction that resolves most of these questions is that bacteriostatic water suppresses microbial growth and does not sterilise anything. It buys you a multiple-withdrawal presentation; it does not make an unsterile preparation sterile, and it does not substitute for technique.
Do not use the same needle to pierce the stopper and to administer.
The practical summary: fine gauge, gentle swirl, diluent down the wall, room temperature before drawing.
Published data on syringe dead space in the context of injection-equipment programmes quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more.
The caveat is that this is not a recommendation to administer anything. Research-use-only material is not approved for human use.
The practical summary: fine gauge, gentle swirl, diluent down the wall, room temperature before drawing, and check the syringe scale.