6.23 Calculating Percentage Uncertainties

• Percentage uncertainties are compounded when multiplying or dividing data

Multiplying / Dividing Data

• Add the percentage or fractional uncertainties

Raising to a Power

• Multiply the percentage uncertainty by the power

Exam Tip

Single Reading

• Percentage uncertainty for a single reading (measured value) is defined by the equation:

Percentage uncertainty = × 100 %

• The (absolute) uncertainty in a single reading is half the resolution of the instrument

Multiple Readings

• The percentage uncertainty in measurements from multiple readings (e.g. repeat readings) use half the range of the readings
  • The range of the readings is the difference between the highest and lowest reading

Worked Example

1. Calculate the mean value 

mean ω = = 0.153 rad s^–1

2. Calculate half the range (this is the uncertainty for multiple readings)

× (0.159 – 0.147) = 0.006 rad s^–1a

3. Calculate percentage uncertainty

× 100 % = × 100 %

× 100 % = 3.92 %

Exam Tip