Measurements & errors

• Absolute uncertainties


  The smallest measurements that can be taken with an instrument
• Exam boards assume absolute uncertainties are half of the smallest measurements
• Digital instruments


  The last digit indicates the absolute uncertainty
• Percentage uncertainty


  Calculated as: (absolute uncertainty / experimental value) x 100
• Reporting measurement with uncertainty

  5.46 volts ± 0.18%
• Finding absolute uncertainty from percentage uncertainty

  1. Percentage uncertainty = 5%

  2. Absolute uncertainty = 5% of 50 volts = 2.5 volts
• Combining uncertainties


  • For adding/subtracting: add absolute uncertainties
  • For multiplying/dividing: add percentage uncertainties
  • For raising to a power: multiply percentage uncertainty by the power
• Random errors

  Completely unpredictable, can produce anomalous results. Usually only affects one or two results.
• Systematic errors

  Often caused by you/your equipment - entire set of data is affected.