[hazbot]

I learnt this way of thinking about units in my engineering degree, and it is indeed incredibly powerful and I regularly use it.

But I would classify it as "algebra" instead of "arithmetic". Being fluent in manipulations like

60 km/h = 60 km/h * h/3600s * 1000m/km

is not a trivial modality of thought to unlock!

[downboots]

https://en.wikipedia.org/wiki/Dimensional_analysis