Units & measures

Unit work is pure marks if you are careful. The specification expects fluency with SI prefixes and compound units, and the ability to convert between related units in both numerical and algebraic contexts.

Know these by heart: nano $10^{-9}$, micro $10^{-6}$, milli $10^{-3}$, centi $10^{-2}$, deci $10^{-1}$, kilo $10^3$, mega $10^6$, giga $10^9$.

A negative index in a unit means "per": ${\text{m s}}^{-1}$ is metres per second, ${\text{kg m}}^{-3}$ is kilograms per cubic metre.

Compound units combine base units. The three that appear most:

• Speed $=\frac{\text{distance}}{\text{time}}$ (m s⁻¹)
• Density $\rho =\frac{\text{mass}}{\text{volume}}$ (kg m⁻³)
• Pressure $P=\frac{\text{force}}{\text{area}}$ (N m⁻² = Pa)

For areas the conversion factor is squared, and for volumes it is cubed. Since $1\text{ m}=100\text{ cm}$:

• $1{\text{ m}}^2=100^2=10^4{\text{ cm}}^2$
• $1{\text{ m}}^3=100^3=10^6{\text{ cm}}^3$

• Converting area/volume with a plain factor instead of squaring/cubing it.
• Mixing units inside one calculation (e.g. cm with m); convert first.
• Dropping the unit and so not noticing an answer is a factor of $1000$ out.