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Errors and uncertainties Cambridge International AS & A Level Physics revision

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In plain words

No measurement is exact. A ruler reads to the nearest millimetre; a stopwatch depends on your reactions. An uncertainty says how far out a value might be, and when you calculate with measurements, their uncertainties combine in a definite way.

Three things to know

  1. A random error scatters readings either side of the true value: reduce it by repeating and averaging. A systematic error shifts every reading the same way (a zero error): averaging doesn't help.
  2. Percentage uncertainty = absolute uncertainty ÷ value × 100.
  3. Adding or subtracting quantities: add the absolute uncertainties. Multiplying or dividing: add the percentage uncertainties. Raising to a power: multiply the percentage uncertainty by the power.

Worked example

A distance is 2.50 ± 0.01 m and a time is 1.20 ± 0.02 s. Find the speed and its uncertainty.

  1. Speed = 2.50 ÷ 1.20 = 2.08 m/s.
  2. Percentage uncertainties: 0.01 ÷ 2.50 = 0.4%, and 0.02 ÷ 1.20 = 1.7%. Dividing, so add: 2.1%.
  3. 2.1% of 2.08 is 0.04. Speed = 2.08 ± 0.04 m/s.

Tips and tricks

  • Precision is how close repeated readings are to each other. Accuracy is how close they are to the true value.
  • Quote an uncertainty to one significant figure, and the value to the same decimal place.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Errors and uncertainties: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is the effect of a systematic error?
    • It scatters readings randomly.
    • It shifts all readings in the same direction. (the answer)
    • It disappears when readings are averaged.
    • It only affects the first reading.

    A zero error on a balance is an example.

  2. How can the effect of random errors be reduced?
    • by using a different unit
    • by repeating readings and taking a mean (the answer)
    • by subtracting a constant
    • it cannot be reduced

    Random scatter averages out.

  3. What is the percentage uncertainty in 20.0 ± 0.5 V?
    • 0.5%
    • 2.5% (the answer)
    • 5%
    • 10%

    0.5 ÷ 20.0 × 100.

  4. The side of a cube has a 1% uncertainty. What is the percentage uncertainty in its volume?
    • 1%
    • 2%
    • 3% (the answer)
    • 9%

    Volume is side cubed.

  5. Two lengths, 10.0 ± 0.1 cm and 4.0 ± 0.1 cm, are subtracted. What is the uncertainty in the result?
    • 0
    • ± 0.1 cm
    • ± 0.2 cm (the answer)
    • ± 0.01 cm

    Absolute uncertainties add, even when the quantities are subtracted.

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