A way that I've found to avoid "cursing" units is to always include what they refer to, into the equations. A good example of that is concentration per weight:
- not including it - "brine is 28% g/g" → "brine is 28%, unitless" → "brine is 28%... uh... was I measuring it through volume, weight, or molarity?"
- including it - "brine is 28% (g solute)/(g solution)" (and you can't cancel the units out as they're different.)
This solves a lot of cursed examples from the video:
- fuel economy - you can list it in (L fuel)/(km road), (km road)/(L fuel), or even (m³ fuel)/(m road). But you can't really divide the later, as 1∛(m³ fuel)' is not the same as 1(m road).
- km/s/Mpc - 1 Hz is not just 1/s, but rather (1 event)/s. So unless you're dealing with the time between events, you don't use Hz, period; at most s⁻¹
IMO kWh=k(J/s)*h is silly though. It would be simpler if power was listed in MJ/h, and then consumption in MJ; sticking to simpler units whenever possible.
The one for dispersion feels fishy; is dispersion really expected to be measured by the square root of length?