1-Measurements and errors

• Standard Si units:

  • mass = kilograms
  • length = meters
  • time = seconds
  • electrical current = amps
  • temperature = kelvin
  • amount of substance = mol
• Standard form is used for either very large or very small numbers.
• prefixes:

  • tetra = 10 to the 12
  • giga = 10 to the 9
  • mega = 10 to the 6
  • kilo = 10 to the 3
  • centi = 10 to the -2
  • milli = 10 to the -3
  • micro = 10 to the -6
  • nano = 10 to the -9
  • pico = 10 to the -12
  • fento = 10 to the -15
• when uncertainties are given as a fixed number than they are an absolute uncertainty.
• when uncertainties are given as a percentage they are a percentage uncertainty.
• when uncertainties are added or subtracted:

  • add the absolute uncertainty
• when multiplying or dividing:

  • add the percentage uncertainty
• when raised to a power:

  • times uncertainty by the power value
• error bars represent uncertainties on a graph
• there are two lines of worst fit that can be drawn:

  • one with steepest gradient
  • one with shallowest gradient
• to find the uncertainty in the gradient of a graph find the biggest difference between the best and worst fit lines. this same rule applies for intercepts.
• Random errors cause measurements to be spread about the true value , due to results varying in a unpredictable way from one measurement to the next.
• Random errors cannot be corrected , only the effect caused reduced by making more measurements and calculating the mean.
• systematic errors cause readings to be different from the true value by a constant amount.
• A zero error is when an instrument does not read zero when it should.
• systematic errors need to be identified before they can be reduced . they can be reduced by repeating the experiment with a different apparatus and or method.
• Accuracy is where measurements are close to true value
• precision is where results have little spread about the mean
• repeatability is where the same measurements are obtained when the same person repeats the experiment using the same method and equipment.
• reproducibility is where similar measurements can be obtained when a different person repeats the experiment using a different method and or equipment.