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Calculating Uncertainties (CIE AS Physics)

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Calculating uncertainty

What is uncertainty?

  • There is always a degree of uncertainty when measurements are taken; the uncertainty can be thought of as the difference between the actual reading taken (caused by the equipment or techniques used) and the true value
  • Uncertainties are not the same as errors
    • Errors can be thought of as issues with equipment or methodology that cause a reading to be different from the true value
    • The uncertainty is a range of values around a measurement within which the true value is expected to lie, and is an estimate
  • For example, if the length of a box is measured multiple times as 12.55 cm, 12.45 cm and 12.51 cm, we can say the length is 12.50 cm with an uncertainty of 0.05 cm,
    • This is often written as 12.50 ± 0.05 cm

Calculating Uncertainty

  • Uncertainties can be represented in a number of ways:
    • Absolute Uncertainty: where uncertainty is given as a fixed quantity (as above)
    • Fractional Uncertainty: where uncertainty is given as a fraction of the measurement
    • Percentage Uncertainty: where uncertainty is given as a percentage of the measurement

p e r c e n t a g e space u n c e r t a i n t y space equals space fraction numerator a b s o l u t e space u n c e r t a i n t y space over denominator m e a s u r e d space v a l u e end fraction space cross times space 100 percent sign

  • To find uncertainties in different situations:
    • The uncertainty in a reading (e.g. from a voltmeter): ± half the smallest division
    • The uncertainty in a measurement (e.g. from a ruler): at least ±1 smallest division
    • The uncertainty in repeated data: half the range i.e. ± ½ (largest - smallest value)
    • The uncertainty in digital readings: ± the last significant digit unless otherwise quoted

Diagram showing a reading from an ammeter

Calculating Uncertainties, downloadable AS & A Level Physics revision notes

Combining uncertainties

  • When combining two measurements that both have uncertainties, the uncertainties have to be combined too

Adding or subtracting data

  • When adding or subtracting two values with uncertainties, just add the absolute uncertainties

Adding or subtracting data example

Combining Uncertainties (1), downloadable AS & A Level Physics revision notes

Multiplying or dividing data

  • When multiplying or dividing measurements with uncertainties, add their fractional or percentage uncertainties

Multiplying or dividing data example

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

  • When the measurement is raised to a power, multiply the fractional or percentage uncertainty by the power

Raising to a power example

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

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Ashika

Author: Ashika

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Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.