Uncertainties

• SI units

  The International System of Units, used worldwide
• 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
• Derived units

  Units derived from combinations of base units, e.g. velocity (m/s), acceleration (m/s^2), force (N = kg·m/s^2), energy (J = kg·m^2/s^2)
• Prefixes

  Used to represent very large and very small numbers, e.g. tera (10^12), giga (10^9), milli (10^-3), nano (10^-9)
• Electron volt


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


  A unit of energy equal to 3.6 x 10^6 joules, used for household electricity
• Measurement errors


  • Random errors (small spread around true value)
  • Systematic errors (consistent difference from true value)
• Accuracy


  How close a result is to the true value
• Precision


  How close repeated readings are to each other
• Repeatability


  Getting the same results when repeating an experiment
• Reproducibility


  Getting the same results using a different method or by other people
• Resolution


  The smallest change that can be detected by the measuring instrument
• Uncertainty


  The range within which the true value is expected to lie, represented by absolute uncertainty (with units) or percentage uncertainty
• Readings vs Measurements

  Readings are single judgements, e.g. from a thermometer or digital meter. Measurements involve two judgements, e.g. using a ruler or protractor.
• Analog meters


  Have a zero point where you have to set the dial at the beginning
• Single judgement reading

  Absolute uncertainty is plus or minus half of the smallest scale division
• Ruler

  Absolute uncertainty is plus or minus 1 millimeter (start point judged to 0.5mm, end point judged to 0.5mm)
• Percentage uncertainty in a single reading

  Absolute uncertainty divided by measured value, multiplied by 100
• Percentage uncertainty in repeated readings

  Half the range divided by the mean, multiplied by 100
• Drawing graphs


  1. Choose appropriate scale

  2. Plot data points

  3. Draw line of best fit

  4. Add error bars
• Line of best fit


  Drawn to go through the centre of the data points
• Worst acceptable line of best fit


  Still goes through the error bars, but not as good as the true line of best fit
• Percentage uncertainty in gradient

  Difference between best and worst line of best fit gradients, divided by best gradient, multiplied by 100
• Percentage uncertainty in y-intercept


  Difference between best and worst line of best fit y-intercepts, divided by best y-intercept, multiplied by 100
• Combining percentage uncertainties

  If X = Y + Z, then percentage uncertainty in X = percentage uncertainty in Y + percentage uncertainty in Z
• Estimating values


  Using common values and orders of magnitude to estimate unknown quantities