Imagine you are baking a cake.
The recipe says: "Mix 200 g flour, 100 g sugar, and bake for 30 minutes at 180°C." Every ingredient has a unit — grams, minutes, degrees. If you mix up grams with ounces, your cake fails. Physics works exactly the same way.
Units are labels on numbers. A speed of "5" means nothing — 5 metres per second and 5 kilometres per hour are completely different things. The SI system is humanity's agreement to use the same labels.
Dimensional analysis is checking your recipe. If a physics formula says "add a force to a distance," that's like adding grams to minutes — it makes no sense. Every term in a valid equation must have identical dimensions.
Significant figures are about honesty. If you weigh yourself on a bathroom scale (reads to 1 kg), writing "73.4567 kg" is dishonest — your scale cannot know all those decimal places. Significant figures tell you how many digits you actually measured, not guessed.
Error propagation is about spreading uncertainty. Suppose you measure a room's width as 5.0 ± 0.1 m and its length as 8.0 ± 0.1 m. The area is 40 , but your uncertainty is: (0.1/5.0 + 0.1/8.0) × 40 = (0.02 + 0.0125) × 40 = 1.3 . So the room is 40 ± 1.3 . Every measurement carries a "cloud of uncertainty" that spreads through every calculation.