Determining Uncertainty (Edexcel International A Level Physics)

Revision Note

Katie M

Author

Katie M

Expertise

Physics

Percentage Uncertainty in Single Readings

  • 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 %

Worked example

A student measures the potential difference on an analogue voltmeter with resolution 0.2 V as 15 V. 

Calculate the percentage uncertainty in the student's reading of the potential difference.

1. Determine the absolute uncertainty

    • The absolute uncertainty of the reading is half the resolution of the analogue voltmeter

fraction numerator 0.2 over denominator 2 end fraction= 0.1 V

2. Calculate the percentage uncertainty

fraction numerator 0.1 over denominator 15 end fraction× 100 % = 0.67 %

Exam Tip

Always make sure your percentage uncertainty is at least one significant figure smaller than the measurement.

Percentage Uncertainty in 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 fraction0.153 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!

You will not be expected to compound percentage uncertainties for AS.

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Katie M

Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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