When a result is calculated from several measured quantities, their uncertainties combine. AQA uses three rules.1. Adding or subtracting: add the absolute uncertainties. Two lengths of 12.3 ± 0.1 cm and 4.5 ± 0.1 cm have a difference of 7.8 ± 0.2 cm. The uncertainties still add when you subtract.2. Multiplying or dividing: add the percentage uncertainties.3. Raising to a power: multiply the percentage uncertainty by the power. For y = xn:% uncertainty in y = n × % uncertainty in x Multiplying by an exact constant (such as π or ½) does not change the percentage uncertainty.Worked example: A resistor has V = 6.0 ± 0.1 V and I = 0.50 ± 0.01 A.
% uncertainty in V = 0.1 ÷ 6.0 × 100% = 1.7%
% uncertainty in I = 0.01 ÷ 0.50 × 100% = 2.0%
R = V ÷ I = 12 Ω, with a percentage uncertainty of 1.7% + 2.0% = 3.7%.
Absolute uncertainty = 3.7% of 12 Ω = 0.44 Ω, so R = 12.0 ± 0.4 Ω.Power example: A circle has radius r = 2.0 ± 0.1 cm, a 5% uncertainty. The area A = πr2 has a percentage uncertainty of 2 × 5% = 10%.Always convert back to an absolute uncertainty at the end, and quote it to one or two significant figures.
% uncertainty in V = 0.1 ÷ 6.0 × 100% = 1.7%
% uncertainty in I = 0.01 ÷ 0.50 × 100% = 2.0%
R = V ÷ I = 12 Ω, with a percentage uncertainty of 1.7% + 2.0% = 3.7%.
Absolute uncertainty = 3.7% of 12 Ω = 0.44 Ω, so R = 12.0 ± 0.4 Ω.Power example: A circle has radius r = 2.0 ± 0.1 cm, a 5% uncertainty. The area A = πr2 has a percentage uncertainty of 2 × 5% = 10%.Always convert back to an absolute uncertainty at the end, and quote it to one or two significant figures.