Edexcel International A Level Physics

Revision Notes

International A LevelPhysicsEdexcelRevision Notes6. Practical Skills in Physics IIPractical Skills II: Analysis6.23 Calculating Percentage Uncertainties

6.23 Calculating Percentage Uncertainties

Test Yourself

Percentage Uncertainties

  • Percentage uncertainties are compounded when multiplying or dividing data

Multiplying / Dividing Data

  • Add the percentage or fractional uncertainties

Combining Uncertainties (2), downloadable AS & A Level Physics revision notes

Raising to a Power

  • Multiply the percentage uncertainty by the power

Combining Uncertainties (3), downloadable AS & A Level Physics revision notes

Exam Tip

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 = fraction numerator u n c e r t a i n t y over denominator m e a s u r e d space v a l u e end fraction× 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.

1. Calculate the mean value 

mean ω = fraction numerator 0.154 thin space plus thin space 0.153 space plus thin space 0.159 thin space plus thin space 0.147 space plus thin space 0.152 over denominator 5 end fraction= 0.153 rad s–1

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

1 half× (0.159 – 0.147) = 0.006 rad s–1a

3. Calculate percentage uncertainty

fraction numerator u n c e r t a i n t y over denominator m e a s u r e d space v a l u e end fraction × 100 % = fraction numerator plus-or-minus h a l f space t h e space r a n g e over denominator m e a n end fraction × 100 %

fraction numerator 0.006 over denominator 0.153 end fraction× 100 % = 3.92 %

Exam Tip

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.

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