Converting Units

Calculations must use consistent SI units, so you often need to convert values first. AQA expects you to convert between these common units:Energy: 1 eV = 1.60 × 10⁻¹⁹ J (the energy gained by an electron accelerated through 1 V), and 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.Areas and volumes: square or cube the conversion factor as well as the unit. Since 1 cm = 10⁻² m:1 cm² = (10⁻² m)² = 10⁻⁴ m²    1 cm³ = 10⁻⁶ m³    1 mm² = 10⁻⁶ m²Speed: 1 km h⁻¹ = 1000 m / 3600 s, so divide km h⁻¹ by 3.6 to get m s⁻¹.Density: 1 g cm⁻³ = 10⁻³ kg / 10⁻⁶ m³ = 1000 kg m⁻³.Worked example 1: 72 km h⁻¹ = 72 / 3.6 = 20 m s⁻¹.Worked example 2: aluminium has density 2.7 g cm⁻³ = 2.7 × 1000 = 2700 kg m⁻³.Worked example 3: a photon has energy 5.0 eV. In joules, 5.0 × 1.60 × 10⁻¹⁹ = 8.0 × 10⁻¹⁹ J.A good check: converting to a smaller unit gives a bigger number. Write the units at every step so that any missing factor shows up.