Physical quantities and sensible estimates

By the end of this lesson

By the end you can explain why a physical quantity needs both a number and a unit, and make sensible estimates of everyday quantities from a handful of reference values.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$l$	length
$v$	speed
$V$	volume

A number on its own means nothing

A physical quantity is anything you can measure: mass, time, current, pressure… It is always written as a numerical magnitude multiplied by a unit:

$g = 9.81\ \text{m s}^{-2}$

"9.81" is the magnitude; $\text{m s}^{-2}$ is the unit. Drop the unit and the number is useless. "The bench is 2.4 long" could mean 2.4 mm or 2.4 km, which differ by a factor of a million.

Because the unit is literally multiplied by the number, you can treat it like an algebra symbol. If $l = 2.4\ \text{m}$ then $l / \text{m} = 2.4$ . That is why table headings and graph axes are written as quantity / unit, such as " $l$ / m" or " $t$ / s".

Definition

Physical quantity

A measurable property, expressed as a numerical magnitude multiplied by a unit, for example $v = 25\ \text{m s}^{-1}$ .

Quick check

One-line answerQuestion 1 · Recall

Answer the question above to continue.