A measurement is written as a value with an uncertainty, for example a wire diameter of 0.38 ± 0.01 mm. The true value is expected to lie in this range.The absolute uncertainty is the ± value (0.01 mm here). It is written with the same units as the measurement.The percentage uncertainty compares the absolute uncertainty with the size of the measurement:percentage uncertainty = (absolute uncertainty ÷ measured value) × 100% Estimating the absolute uncertainty of a single reading:
• Analogue scale (such as a thermometer): ± half the smallest division.
• Digital meter: ± one in the last digit, for example ±0.01 V for a reading of 3.46 V.
• Length on a ruler, where both ends are read: ± one smallest division.Worked example 1: Diameter = 0.38 ± 0.01 mm.
Percentage uncertainty = 0.01 ÷ 0.38 × 100% = 2.6%.Worked example 2: The time for 10 oscillations of a pendulum is 15.2 ± 0.2 s, a percentage uncertainty of 0.2 ÷ 15.2 × 100% = 1.3%. Dividing by 10 gives a period of 1.52 s with an absolute uncertainty of 0.02 s; the percentage uncertainty is still 1.3%.Worked example 2 shows a useful technique: measuring a larger quantity with the same instrument gives a smaller percentage uncertainty. Timing one oscillation with the same ±0.2 s uncertainty would give over 13%. Percentage uncertainty lets you compare how reliable different measurements are and find which one contributes most to the uncertainty of a final result.
• Analogue scale (such as a thermometer): ± half the smallest division.
• Digital meter: ± one in the last digit, for example ±0.01 V for a reading of 3.46 V.
• Length on a ruler, where both ends are read: ± one smallest division.Worked example 1: Diameter = 0.38 ± 0.01 mm.
Percentage uncertainty = 0.01 ÷ 0.38 × 100% = 2.6%.Worked example 2: The time for 10 oscillations of a pendulum is 15.2 ± 0.2 s, a percentage uncertainty of 0.2 ÷ 15.2 × 100% = 1.3%. Dividing by 10 gives a period of 1.52 s with an absolute uncertainty of 0.02 s; the percentage uncertainty is still 1.3%.Worked example 2 shows a useful technique: measuring a larger quantity with the same instrument gives a smaller percentage uncertainty. Timing one oscillation with the same ±0.2 s uncertainty would give over 13%. Percentage uncertainty lets you compare how reliable different measurements are and find which one contributes most to the uncertainty of a final result.