Singapore-Cambridge O-Level Combined Science (Physics/Chemistry)

## Physical quantities and units A **physical quantity** is something that can be measured, and it is always written as a numerical magnitude together with a unit. A length of 5 means nothing until it is given as 5 m, 5 cm or 5 km, and the number changes with the unit chosen although the length does not. Every physical quantity can be built from a small set of **base quantities**, each with an SI base unit. | Base quantity | SI unit | Symbol | |---|---|---| | Mass | kilogram | kg | | Length | metre | m | | Time | second | s | | Electric current | ampere | A | | Temperature | kelvin | K | | Amount of substance | mole | mol | All other quantities have derived units made from these. Speed is length divided by time, so its unit is $\mathrm{m\,s^{-1}}$ (written m/s in this course). Force is measured in newtons, where $1\ \mathrm{N} = 1\ \mathrm{kg\,m\,s^{-2}}$, and energy in joules, where $1\ \mathrm{J} = 1\ \mathrm{N\,m}$. ### Prefixes Very large and very small values are written with a prefix in front of the unit. Each prefix is a power of ten. | Prefix | Symbol | Multiplies the unit by | |---|---|---| | tera | T | $10^{12}$ | | giga | G | $10^{9}$ | | mega | M | $10^{6}$ | | kilo | k | $10^{3}$ | | deci | d | $10^{-1}$ | | centi | c | $10^{-2}$ | | milli | m | $10^{-3}$ | | micro | µ | $10^{-6}$ | | nano | n | $10^{-9}$ | To convert, replace the prefix by its power of ten. A wavelength of 650 nm is $650 \times 10^{-9}\ \mathrm{m} = 6.5 \times 10^{-7}\ \mathrm{m}$, and a…