Absolute uncertainty
Measurements & Uncertainties - OCR A-Level Physics
Key Definition
Absolute uncertainty
The uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading.
The uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading.
- For a single reading from an instrument: absolute $uncertainty = +/- half$ the smallest division.
- For a set of repeats: absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading. = half the range of the repeat readings.
- Example: readings of 2.34, 2.38, 2.31 s. $Range = 2.38 - 2.31 = 0.07 s. Uncertainty = +/- 0.04 s (half$ the range, rounded up).
- The mean value is (2.34 + 2.38 + 2.31) / 3 = 2.34 s. Result: 2.34 +/- 0.04 s.
$$\text{Percentage uncertainty} = \frac{\text{absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading.}}{\text{measured value}} \times 100\%$$
- Example: $length = 0.45 +/- 0.01 m. Percentage uncertainty = (0.01 / 0.45) x 100% = 2.2%$.
- Percentage uncertainties have no units -- they are dimensionless.
- Small percentage $uncertainty = high-quality measurement$.
Common Mistake
MEDIUM
Wrong: Using the absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading. as the percentage uncertainty (e.g. writing '0.01%' when the absolute uncertainty is 0.01 m).
Right: Percentage $uncertainty = (absolute / measured) x 100%. You must divide$ by the measured value first. 0.01 m out of 0.45 m is 2.2%, not 0.01%.
Right: Percentage $uncertainty = (absolute / measured) x 100%. You must divide$ by the measured value first. 0.01 m out of 0.45 m is 2.2%, not 0.01%.