To understand that every physical quantity is expressed as a product of a numerical magnitude and a unit.
A physical quantity describes a property of the physical world that can be measured. It is represented mathematically as
$$Q = N \times U$$where Q is the quantity, N is the numerical value (a pure number), and U is the unit that gives the quantity its meaning.
The International System of Units (SI) provides a consistent set of base units from which all other units are derived.
| Quantity | Symbol | SI Unit | Unit Symbol |
|---|---|---|---|
| Length | $L$ | metre | m |
| Mass | $m$ | kilogram | kg |
| Time | $t$ | second | s |
| Electric current | $I$ | ampere | A |
| Temperature | $T$ | kelvin | K |
| Amount of substance | $n$ | mole | mol |
| Luminous intensity | $I_v$ | candela | cd |
Derived quantities are formed by combining base quantities according to physical laws. Their units are products or quotients of base units.
| Derived Quantity | Symbol | Definition | SI Unit (symbol) |
|---|---|---|---|
| Velocity | $v$ | $v = \dfrac{s}{t}$ | metre per second (m s⁻¹) |
| Acceleration | $a$ | $a = \dfrac{v}{t}$ | metre per second squared (m s⁻²) |
| Force | $F$ | $F = m a$ | newton (N) |
| Energy | $E$ | $E = F s$ | joule (J) |
| Power | $P$ | $P = \dfrac{E}{t}$ | watt (W) |
When writing a measured quantity, the numerical value and unit must be together, e.g.,
Omitting the unit removes the physical meaning and can lead to serious errors (e.g., the Mars Climate Orbiter failure).