Uncertainties

• Uncertainty


  Anything which causes measurements to deviate from the true value
• Sources of uncertainty


  • Resolution of an instrument limits accuracy, as it must eventually be rounded
• Comparing sources of uncertainty

  Work out the percentage uncertainty: Uncertainty x 100 / Measurement
• Prioritise the largest source of uncertainty when trying to improve methods
• Adding or subtracting uncertainties

  Add the absolute uncertainties
• Multiplying or dividing uncertainties

  Add the percentage uncertainties
• Ways to calculate uncertainty

  • When results are varied, the uncertainty is half the range of values
  • The resolution gives the uncertainty: for a resolution of 1d.p. it is ± 0.05, for a resolution of 2d.p. it is ± 0.005, etc.
  • Plot the data on a graph, draw a line of best fit and a line of worst fit - the difference between the gradients provides the uncertainty
• Base units (SI units)


  • Metre, m
  • Kilogram, kg
  • Second, s
  • Ampere, A
  • Kelvin, K
  • Candela, cd
  • Mole, mol
• All other quantities can be expressed in base units, but in many cases derived units have been developed
• Working out the units of a quantity from equations

  For example, acceleration is equal to change in velocity / time, and the units are m/s^2 (or m/s per s)
• Standard form


  A number with one digit before the decimal place, multiplied by a power of 10
• Using numbers in standard form in mathematical equations

  1. The powers of 10 are added when multiplying

  2. The powers of 10 are subtracted when dividing
• Prefixes


  • Tera (T) x 10^12
  • Giga (G) x 10^9
  • Mega (M) x 10^6
  • Kilo (k) x 10^3
  • Centi (c) x 10^-2
  • Mili (m) x 10^-3
  • Micro (μ) x 10^-6
  • Nano (n) x 10^-9
  • Pico (p) x 10^-12
  • Femto (f) x 10^-12
• Calibration


  Determination of the relationship between input and output, and ensuring that the correct output is produced for a given input
• Noise


  Random variations superimposed onto a signal
• Resolution


  The smallest change that can be detected/displayed by an instrument
• Repeatability


  When a procedure can be repeated by the same person with the same equipment/method to obtain similar results
• Reproducibility


  When a procedure can be repeated by a different person with different methods/equipment to obtain similar results
• Response time


  The time it takes for an instrument to generate an output from an input
• Sensitivity


  The change in output for a unit change in output
• Zero error


  When the output produced by zero input is not zero