Vial to strength
The step before the measurement step. A mass and a diluent volume give a strength, and that strength is a ceiling rather than a measurement unless the finished volume was read off the barrel.
Educational arithmetic only. Not medical advice and not a dosing protocol.
Enter the figures above.
Where that comes from
- Strength is the mass divided by the volume of the FINISHED solution:
strength = mass ÷ V. - The finished solution is the diluent plus the room the dissolved solid takes up. With that displacement unmeasured,
V ≥ diluent, so dividing by the diluent gives the highest the strength can be. - So the figure reads at most until a finished volume is entered, and every volume derived from it reads at least.
- Five milligrams in 2 mL is at most 2.5 mg/mL, which is 2,500 mcg/mL, which is 250 mcg in each tenth of a millilitre.
The bound runs the useful way
A strength that is too high produces a volume that is too small, so a volume derived from a ceiling is the least that could hold the amount. A reader drawing it has not drawn more than intended. Getting the direction of an uncertainty right is worth more than hiding that there was one.
Measuring the finished volume removes the question entirely: mark the barrel after mixing, read the figure, type it in, and the label on the answer changes because the uncertainty it was flagging has gone.
How big the gap is
Small, and it scales with the mass. For a couple of milligrams of solid the displaced volume is a few microlitres, which against a 2 mL diluent volume is a fraction of a percent - well inside the error of reading a 1 mL barrel marked every unit. For thirty milligrams it is larger.
Which is a good argument for not worrying much about it, and not an argument for pretending it is zero. Exact and approximate sets out which figures on this site are measurements, which are bounds and which are floating-point approximations.