Dimensions: a spell-check for formulas

Your friend says the price of 2 kg of mangoes plus 3 hours is 500. You'd laugh — you can't add kilograms to hours. Yet in exams, students write formulas that do exactly that, and lose marks without noticing.

Physics has a built-in spell-check for this. Every quantity is made of a few basic ingredients: mass [M], length [L] and time [T]. These ingredients are called dimensions, and they're always written in square brackets.