Percentage Uncertainty

The uncertainty can be expressed as a percentage of the reading.

Percentage uncertainty = uncertainty /(average value) x 100%

Example. A metre rule that measures a block as 295 mm has an absolute uncertainty of 1mm. What is its percentage uncertainty (2sf)?

Percentage uncertainty = 1 /295 / 100% = 0.34%

Propagation of Uncertainties

Multiplication or division of 2 values: y = ab or y = a / b

% uncertainty in y = % uncertainty in a + % uncertainty in b

Example:

Calculate the percentage uncertainty in force causing a mass of 50kg 10% to accelerate by 20 ms -2 5%.

F = ma

Combined uncertainty = 10% + 5% = 15%

Raising a values to a power: e.g. y = a^exponent

% uncertainty in y = exponent x % uncertainty in a

Example:

Calculate the percentage uncertainty in the volume of a cube of side, L = 4.0cm 2%.

Volume = L3

% uncertainty = 6% (2% x 3)

Calculate the percentage uncertainty in the volume of a cube of side, L = 4.0cm 2%.

Volume = L3

% uncertainty = 6% (2% x 3)