Unit 4 units and Uncertainties

4.1 Units, prefixes and scientific notation

Learning Outcomes

  1. State that measurement of any physical quantity is liable to uncertainty.
  2. Distinguish between random uncertainties and recognised systematic effects.
  3. State that the scale-reading uncertainty is a measure of how well an instrument scale can be read.
  4. Explain why repeated measurements of a physical quantity are desirable.
  5. Calculate the mean value of a number of measurements of the same physical quantity.
  6. State that this mean is the best estimate of a ‘true’ value of the quantity being measured.
  7. State that where a systematic effect is present the mean value of the measurements will be offset from a ‘true’ value of the physical quantity being measured.
  8. Calculate the approximate random uncertainty in the mean value of a set of measurements using the relationship: (maximum reading - minimum reading)/Number of readings.
  9. Estimate the scale-reading uncertainty incurred when using an analogue display and a digital display.
  10. Express uncertainties in absolute or percentage form.
  11. Identify, in an experiment where more than one physical quantity has been measured, the quantity with the largest percentage uncertainty.
  12. State that this percentage uncertainty is often a good estimate of the percentage uncertainty in the final numerical result of the experiment.
  13. Express the numerical result of an experiment in the form: final value ± uncertainty.

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Aids to Understanding


Reading scales.

Suppose you measure a piece of paper with the ruler below and you estimate it is a bit more than twenty two centimeters, say one fifth more. The correct way to write your value is; 22.2 cm. Since the smallest scale division of the ruler is 0.5 cm the scale reading uncertainty is 0.25 cm , but we should round it up (we never round uncertainties down) to 0.3 cm. The reading with uncertainty is written as
(22.2 +/- 0.3) cm. In meters we would write it as (0.222 +/- 0.003) m. It should now be clear that a ruler with 1.0 cm divisions we are justified in taking our reading to three decimal places. Uncertainty example Excercise Suppose a ball is dropped from a height of 3.3000 m five times. Suppose the times on the digital stopwatch were, 0.81 s, 0.92 s, 0.79 s 0.95 s and 0.99 s.
Your job is to write a report identical to the one on the right and find the average speed with its absolute uncertainty.



1) Uncertainties in Measurements

Uncertainty example

2) Random and systematic uncertaintities



3) Scale reading uncertainties

4) Repeated measurements

5) Calculating averages

6) Average values

7) The problem with systematic uncertainties

8) Calculating random uncertainties

9) Absolute and percentage uncertainties

10) Analysing percentage uncertainties

11) Percentage uncertainties in context

12) Writing our answers

Higher Physics .. Unit 4 Uncertaintities .. 4.2 Uncertainties .. BR (2011)