ESAT (Engineering and Science Admissions Test)

## Standard units and prefixes Every quantity has an SI unit: mass in kilograms (kg), length in metres (m), time in seconds (s). Other units are built from these, and a unit with a negative index says "per": a speed of $5\ \mathrm{m\,s^{-1}}$ is 5 metres for every second. The prefixes change a unit by a power of ten. | Prefix | Symbol | Factor | |---|---|---| | nano | n | $10^{-9}$ | | micro | μ | $10^{-6}$ | | milli | m | $10^{-3}$ | | centi | c | $10^{-2}$ | | deci | d | $10^{-1}$ | | kilo | k | $10^{3}$ | | mega | M | $10^{6}$ | | giga | G | $10^{9}$ | A litre is $1000\ \mathrm{cm^3}$, so $1\ \mathrm{m^3} = 1000$ litres, and $1\ \mathrm{dm^3} = 1$ litre. A tonne is 1000 kg. ### Changing units of area and volume A length conversion must be applied once for each dimension. Since $1\ \mathrm{m} = 100\ \mathrm{cm}$, an area converts with $1\ \mathrm{m^2} = 100^2\ \mathrm{cm^2} = 10\,000\ \mathrm{cm^2}$, and a volume with $1\ \mathrm{m^3} = 10^6\ \mathrm{cm^3}$. Converting $3.5\ \mathrm{cm^2}$ to $\mathrm{mm^2}$ gives $3.5 \times 10^2 = 350\ \mathrm{mm^2}$, because each centimetre is 10 millimetres and there are two lengths in an area. ### Compound units A compound unit divides or multiplies two basic ones, and it converts one part at a time. - Speed: $72\ \mathrm{km\,h^{-1}}$ becomes metres per second by $72 \times 1000 \div 3600 = 20\ \mathrm{m\,s^{-1}}$. - Density: $8.0\ \mathrm{g\,cm^{-3}}$ becomes $\mathrm{kg\,m^{-3}}$ by $8.0 \times 10^{-3}\ \mathrm{kg} \div 10^{-6}\…