1.4. Understanding Uncertainties

• What is the primary cause of random uncertainties?

  Unpredictable variations
• Order the sources of random uncertainties from most to least controllable:

  1️⃣ Human Error

  2️⃣ Instrument Precision

  3️⃣ Environmental Factors
• What is the smallest unit an instrument can measure called?

  Instrument Precision
• What is the formula for calculating percentage uncertainty?

  (Uncertainty / Measured value) x 100
• What is the definition of random uncertainties?

  Unpredictable variations in measurements
• Sources of random uncertainties in measurements

  1️⃣ Instrument precision

  2️⃣ Environmental factors

  3️⃣ Human error
• Random uncertainties can be eliminated by taking multiple measurements and calculating the median.

  False
• A lower percentage uncertainty indicates a more precise measurement.

  True
• When adding two lengths, such as 10 ± 0.2 cm and 20 ± 0.3 cm, the combined length is 30 ± 0.5 cm
• Subtracting measurements requires adding absolute uncertainties.

  True
• How do systematic uncertainties affect results compared to random uncertainties?

  Shift results consistently
• Zeros between non-zero digits are always significant.
• Random uncertainties are predictable variations in measurements.

  False
• Match the type of uncertainty with its characteristics:

  Random uncertainties ↔️ Unpredictable variations

  Systematic uncertainties ↔️ Consistent errors

  Instrument precision ↔️ Cause of random uncertainties
• Why can systematic uncertainties not be reduced by taking more measurements?

  They are consistent errors
• A lower percentage uncertainty indicates a more precise measurement.
• When adding measurements, you add absolute uncertainties.


  True
• What is the combined percentage uncertainty when multiplying (10 ± 2%) cm by (20 ± 3%) cm?

  5%
• Trailing zeros with a decimal point are significant
• Percentage uncertainty is calculated as (Uncertainty / Measured value) x 100
• What does a lower percentage uncertainty indicate about a measurement?

  More precise
• What is the formula for calculating percentage uncertainty?

  $Percentage uncertainty =$$(Uncertainty / Measured value) x 100$
• Percentage uncertainty is expressed as a percentage of the measured value
• The rules for propagating uncertainties vary based on the type of operation
• Match the type of uncertainty with its characteristic:

  Random Uncertainties ↔️ Unpredictable variations

  Systematic Uncertainties ↔️ Consistent errors
• Random uncertainties are unavoidable in measurements.


  True
• What is the formula for calculating percentage uncertainty?

  \frac{\text{Uncertainty}}{\text{Measured Value}} \times 100</latex>
• What is parallax error an example of?

  Systematic uncertainty
• What does a lower percentage uncertainty indicate about a measurement?

  More precise measurement
• What are systematic uncertainties caused by?

  Predictable factors
• How do environmental factors contribute to random uncertainties?

  By affecting measurement conditions
• What is an unzeroed balance an example of?

  Instrument calibration error
• What is the formula for calculating percentage uncertainty from data?

  (Uncertainty / Measured value) x 100
• The time measurement in the example has the highest percentage uncertainty.

  False
• How do you combine absolute uncertainties in addition?

  Add absolute uncertainties
• The result of multiplying (10 ± 2%) cm by (20 ± 3%) cm is (200 ± 5)% cm².
• Significant figures indicate the precision of a measurement.


  True
• How should measurements be reported to reflect their precision?

  Appropriate significant figures
• Environmental factors, such as temperature, can cause random uncertainties.


  True
• Addressing systematic uncertainties improves the overall accuracy of an experiment.


  True