Measurement Uncertainty

Definition

• Measurement uncertainty arises from the imprecision of measuring devices.
• All measuring devices have some level of uncertainty.

Determining Measurement Uncertainty

• It is the larger of the following:
  • Limit of Instrument: Half of the smallest increment multiplied by the number of measurements taken.
  • Experimenter's Estimation: A justified estimation of the measurement procedure's limit.

Real-life Example: Measuring a Pencil with a Ruler

• Limit of Instrument:
  • Smallest increment is 0.5 cm (lines for every 0.5 cm on ruler).
  • Measurement includes two points on the pencil (left and right), therefore 2 measurements.
  • Uncertainty = 0.5 cm x 2 = 0.5 cm.
• Recording Measurement:
  • Example: Length of pencil = 4.3 ± 0.5 cm.

Reading a Meter (Example: Voltage Meter)

• Smallest Increment: 0.2 volts (V).
• Two measurements are taken similar to the ruler example.
• Uncertainty = 0.2 volts.
• Recording Measurement:
  • Example: Voltage = 3.3 ± 0.2 volts.

Digital Readings

• Uncertainty: At least ± one digit of the last significant figure.
• Example: Digital Scale
  • Reading: 163.4 grams.
  • Uncertainty: ± 0.1 grams (last significant figure is 4).
  • Recorded Measurement: 163.4 ± 0.1 grams.

Application in Lab Reports

• When explaining measurement uncertainty in a report:
  • Describe the method used to determine uncertainty as explained above.