measurements & their errors

• Base units

  • Mass
  • Length
  • Time
  • Amount of something
  • Temperature
  • Current
• Units for base quantities

  • Mass: kilograms
  • Length: meters
  • Time: seconds
  • Amount: moles
  • Temperature: Kelvin
  • Current: amps
• Prefixes

  • Tera (10^12)
  • Giga (10^9)
  • Mega (10^6)
  • Kilo (10^3)
  • Milli (10^-3)
  • Micro (10^-6)
  • Nano (10^-9)
  • Pico (10^-12)
  • Femto (10^-15)
• Electron volt

  Energy required to accelerate an electron through a potential difference of 1 volt
• Kilowatt hour

  Energy transferred by a power of 1 kilowatt over 1 hour
• Random error

  Spread of data around the true value, reduced by repeating measurements
• Systematic error

  Consistent difference from the true value, addressed by changing method or equipment
• Key terms

  • Accuracy
  • Precision
  • Repeatability
  • Reproducibility
  • Resolution
• Uncertainty

  Absolute uncertainty (with units) and percentage uncertainty, account for errors in measurements
• Reading vs Measurement

  Reading is a single judgement (e.g. thermometer), measurement involves two judgements (e.g. ruler)
• Analog meter

  Meter where you have to judge the start and end point, leading to uncertainty
• Absolute uncertainty

  Plus or minus half the smallest scale division
• Percentage uncertainty (single reading)

  Absolute uncertainty / measured value x 100
• Percentage uncertainty (repeated readings)

  Half the range / mean x 100
• Drawing graphs

  1. Choose appropriate scale

  2. Label axes with quantity and units

  3. Plot data points

  4. Draw line of best fit

  5. Add error bars
• Line of best fit (LoB)

  Line that goes through the centre of the data points
• Worst acceptable line of best fit (LoB)

  Line that still goes through the error bars, but is not as good as the LoB
• Percentage uncertainty in gradient

  (Gradient of LoB - Gradient of worst LoB) / Gradient of LoB x 100
• Percentage uncertainty in y-intercept

  (y-intercept of LoB - y-intercept of worst LoB) / y-intercept of LoB x 100
• Combined/final uncertainty

  Absolute uncertainties added together if adding/subtracting

  Percentage uncertainties added together if multiplying/dividing
• Estimation uses common values to estimate the size of a final answer