Dilute a stock

C₁V₁ = C₂V₂ answers a single step, and the number you actually pipette is the diluent — the final volume minus the stock. The practical limit is the pipette, not the arithmetic: below about 5 µL the error on the instrument becomes a real fraction of the dose, and below 1 µL it dominates. If a single step asks for less than that, make an intermediate dilution and take a measurable volume of it.

That is also the case for going a long way. A 1 in 10,000 dilution in one step means taking 1 µL into 10 mL, where one bubble ruins it. Four tenfold steps get to the same place with volumes you can see, and the errors partly cancel rather than compounding on a single bad transfer.

Serial dilutions carry their own trap: every step inherits the one before it. Mix each tube properly before drawing from it, and change tips between steps, or you are quietly carrying concentrated stock down the row on the outside of the tip.