Physical quantities and estimation

The big idea

Physics describes the world with numbers, but a number alone tells you nothing. "The rope is 4" could mean 4 mm or 4 km. Every measurement needs a number and a unit together. Once you think this way, you can also do something very useful: make a quick, sensible guess at the size of almost anything before you calculate it exactly.

Explained simply

A physical quantity is anything that can be measured. It is written as a numerical magnitude (the number) multiplied by a unit (the agreed standard you are counting in):

$\text{physical quantity} = \text{numerical magnitude} \times \text{unit}$

So a mass of 3.5 kg really means $3.5 \times 1\ \text{kg}$. This is why you can treat units like algebra. You multiply and divide them along with the numbers, and you must never drop them halfway through a calculation.