Calculating Percentage Uncertainties (Edexcel IAL Physics)

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 Hint Remember:

• Percentage uncertainties have no units
• The uncertainty in numbers and constants, such as π, is taken to be zero

In Edexcel International A level, the uncertainty should be stated to at least one few significant figures than the data but no more than the significant figures of the data.

For example, the uncertainty of a value of 12.0 which is calculated to be 1.204 can be stated as 12.0 ± 1.2 or 12.0 ± 1.20.

Single & Multiple Readings

Single Reading

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

Percentage uncertainty =$\frac{uncertainty}{measured value}$× 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 A student achieves the following results in their experiment for the angular frequency, ω.

0.154, 0.153, 0.159, 0.147, 0.152

Calculate the percentage uncertainty in the mean value of ω.

Answer:

Step 1: Calculate the mean value

mean ω = $\frac{0.154+0.153+0.159+0.147+0.152}{5}$= 0.153 rad s^–1

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

$\frac{1}{2}$× (0.159 – 0.147) = 0.006 rad s^–1a

Step 3: Calculate percentage uncertainty

$\frac{uncertainty}{measured value}$ × 100 % = $\frac{\pm half the range}{mean}$ × 100 %

$\frac{0.006}{0.153}$× 100 % = 3.92 %

Exam Hint Remember that percentage uncertainties have no units, only the % sign! Always make sure your percentage uncertainty is at least one significant figures smaller than the measurement.