SI base units you must know

• Mass uses the kilogram, symbol $\mathrm{kg}$; length uses the metre, symbol $\mathrm{m}$; time uses the second, symbol $\mathrm{s}$.

• Electric current uses the ampere, symbol $\mathrm{A}$; temperature uses the kelvin, symbol $\mathrm{K}$; amount of substance uses the mole, symbol $\mathrm{mol}$.

• These are the six fundamental quantities and associated SI base units required for AQA.

• The SI also includes the candela, symbol $\mathrm{cd}$, but AQA explicitly excludes it from this subtopic.

• Students are not expected to recall formal definitions of the fundamental quantities.

The diagram shows all seven SI base-unit symbols. For AQA, learn $\mathrm{m}$, $\mathrm{kg}$, $\mathrm{s}$, $\mathrm{A}$, $\mathrm{K}$ and $\mathrm{mol}$; $\mathrm{cd}$ is excluded. Source

How derived SI units are formed

• A derived SI unit is formed from products or powers of SI base units.

• Speed may be written as $\mathrm{m,s^{-1}}$ and acceleration as $\mathrm{m,s^{-2}}$.

• The newton is a derived unit: $\mathrm{N}=\mathrm{kg,m,s^{-2}}$.

• The joule is a derived unit: $\mathrm{J}=\mathrm{kg,m^2,s^{-2}}$.

• The watt is a derived unit: $\mathrm{W}=\mathrm{J,s^{-1}}=\mathrm{kg,m^2,s^{-3}}$.

• Recognise that named derived units can be rewritten using base units.

Prefixes and standard form

• An SI prefix represents a multiplying factor expressed as a power of ten.

• To remove a prefix, replace it by its corresponding power of ten.

• For example, $7.2,\mathrm{mm}=7.2\times10^{-3},\mathrm{m}$.

• Similarly, $4.5,\mathrm{\mu s}=4.5\times10^{-6},\mathrm{s}$.

• To introduce a prefix, reverse the process: $3.6\times10^{-9},\mathrm{m}=3.6,\mathrm{nm}$.

• Always check the sign of the exponent and the case of the prefix symbol.

Joule and electronvolt conversions

• The joule and electronvolt are both units used for energy, so AQA may require conversion between them.

• Use $1,\mathrm{eV}=1.602176634\times10^{-19},\mathrm{J}$.

• For examination calculations, this is commonly used as approximately $1,\mathrm{eV}=1.60\times10^{-19},\mathrm{J}$.

• To convert from $\mathrm{eV}$ to $\mathrm{J}$, multiply by $1.60\times10^{-19}$.

• To convert from $\mathrm{J}$ to $\mathrm{eV}$, divide by $1.60\times10^{-19}$.

• For example, $5.0,\mathrm{eV}\approx8.0\times10^{-19},\mathrm{J}$.

What AQA excludes

• The candela, symbol $\mathrm{cd}$, is not required for this subtopic.

• Formal definitions of the fundamental quantities do not need to be recalled.

• Dimensional analysis is not required.

• Focus instead on using the required units, prefixes, standard form and unit conversions accurately.

Large SI prefixes

• Tera, symbol $\mathrm{T}$, represents $10^{12}$.

• Giga, symbol $\mathrm{G}$, represents $10^{9}$.

• Mega, symbol $\mathrm{M}$, represents $10^{6}$.

• Kilo, symbol $\mathrm{k}$, represents $10^{3}$.

• Prefix symbols are case-sensitive; for example, $\mathrm{M}$ and $\mathrm{m}$ represent completely different factors.Large SI prefixes

• Tera, symbol $\mathrm{T}$, represents $10^{12}$.

• Giga, symbol $\mathrm{G}$, represents $10^{9}$.

• Mega, symbol $\mathrm{M}$, represents $10^{6}$.

• Kilo, symbol $\mathrm{k}$, represents $10^{3}$.

• Prefix symbols are case-sensitive; for example, $\mathrm{M}$ and $\mathrm{m}$ represent completely different factors.

Small SI prefixes

• Centi, symbol $\mathrm{c}$, represents $10^{-2}$.

• Milli, symbol $\mathrm{m}$, represents $10^{-3}$.

• Micro, symbol $\mathrm{\mu}$, represents $10^{-6}$.

• Nano, symbol $\mathrm{n}$, represents $10^{-9}$.

• Pico, symbol $\mathrm{p}$, represents $10^{-12}$.

• Femto, symbol $\mathrm{f}$, represents $10^{-15}$.

Same-quantity unit conversions

• Convert between different units only when they describe the same physical quantity.

• For example, $2.4,\mathrm{km}=2.4\times10^{3},\mathrm{m}$.

• Also, $350,\mathrm{\mu A}=350\times10^{-6},\mathrm{A}=3.50\times10^{-4},\mathrm{A}$.

• A smaller unit gives a larger numerical value; a larger unit gives a smaller numerical value.

• Use standard form to reduce errors when very large or very small factors are involved.