(1.2) Limitation of Physical Measurements

• What are random errors and how do they affect measurements?

  • Affect precision
  • Cause spread about the mean
  • Cannot be completely eliminated
• How can random errors be reduced?

  • Take at least 3 repeats
  • Use computers/data loggers
  • Use appropriate equipment
• What are systematic errors and how do they affect measurements?

  • Affect accuracy
  • Cause consistent bias in results
  • Can be identified and corrected
• How can systematic errors be reduced?

  • Calibrate apparatus
  • Correct for background radiation
  • Read meniscus at eye level
• What is precision in measurements?

  • Consistent measurements
  • Fluctuate slightly around a mean
  • Does not indicate accuracy
• What does repeatability in experiments mean?

  Same results with same methods
• What does reproducibility in experiments mean?

  Same results by different experimenters
• What is resolution in measurements?

  Smallest change that gives a reading
• What is accuracy in measurements?

  Measurement close to the true value
• What is uncertainty in a measurement?

  Bounds in which accurate value lies
• What is absolute uncertainty?

  Fixed quantity uncertainty
• What is fractional uncertainty?

  Uncertainty as a fraction of measurement
• What is percentage uncertainty?

  Uncertainty as a percentage of measurement
• How can you reduce percentage and fractional uncertainty?

  • Measure larger quantities
• What is the uncertainty in a reading?

  ± half the smallest division
• What is the uncertainty in a measurement?

  At least ±1 smallest division
• How is uncertainty in digital readings determined?

  Quoted or assumed ± last significant digit
• How is uncertainty calculated for repeated data?

  Half the range of values
• How can uncertainty be reduced in measurements?

  • Fix one end of a ruler
  • Measure multiple instances
• How should uncertainties be reported?

  Same significant figures as data
• How do you combine uncertainties when adding or subtracting data?

  • Add absolute uncertainties
• What is the difference in temperature if a thermometer shows 298 ± 0.5 K and 273 ± 0.5 K?

  25 ± 1 K
• How do you combine uncertainties when multiplying or dividing data?

  • Add percentage uncertainties
• What is the acceleration if a force of 91 ± 3 N is applied to a mass of 7 ± 0.2 kg?

  $13 \pm 0.8 \text{ m/s}^2$
• How do you calculate percentage uncertainty when raising to a power?

  • Multiply percentage uncertainty by power
• What is the percentage uncertainty in the area of a circle with radius $5 \pm 0.3 \text{ cm}$?


  $12\% \text{ of } 78.5 \text{ cm}^2$
• How are uncertainties represented on graphs?

  • Shown as error bars
  • Line of best fit should go through error bars
• How is the uncertainty in a gradient determined?

  • By lines of best and worst fit
  • Difference between best and worst gradients
• How do you calculate percentage uncertainty in a gradient?

  • Use best and worst gradients
  • Formula: $\frac{100\% \times |best - worst|}{best}$
• How do you find the uncertainty in a y-intercept?

  • Calculate difference between best and worst y-intercepts