Dimensional Analysis (Unit Conversion Chain)

Convert a quantity through a chain of conversion factors so that unwanted units cancel, preventing unit-driven dosing errors. Each factor can be flipped so the units cancel correctly.

$$Q_{\text{out}}=Q_{\text{in}}\times \prod _i{\left(\frac{\text{target unit}}{\text{starting unit}}\right)}_i$$

Variables

Symbol	Meaning	Unit
$Q_{\text{out}}$	Final quantity in target units	varies
$Q_{\text{in}}$	Starting quantity	varies

Worked example

8 fl oz x (29.5735 mL / 1 fl oz) = 236.588 mL, then x (1.00 g / 1 mL) = 236.588 g, then / (18.015 g/mol) = 13.13 mol, then x (6.022 x 10^23 molecules/mol) = 7.91 x 10^24 molecules of water.

---

Part of The Blueprint of Water