Calculating Uncertainties

• What is the definition of uncertainty in measurements?

  Difference between actual reading and true value
• How are uncertainties different from errors?

  Errors are issues causing incorrect readings
• What does uncertainty represent in measurements?

  A range of values around a measurement
• If the true value of a mass is 950 g and the reading is 952 g, what is the uncertainty?

  ±2 g
• What are the different ways to represent uncertainties?

  • Absolute Uncertainty: fixed quantity
  • Fractional Uncertainty: fraction of measurement
  • Percentage Uncertainty: percentage of measurement

  
• How do you find the uncertainty in a reading?

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

  At least ±1 smallest division
• How is uncertainty calculated in repeated data?

  Half the range: ± ½ (largest - smallest)
• What is the uncertainty in digital readings?

  ± the last significant digit
• How should absolute or percentage uncertainty be expressed?

  Same number of significant figures as reading
• What are the rules for combining uncertainties?

  • Adding/Subtracting: Add absolute uncertainties
  • Multiplying/Dividing: Add percentage or fractional uncertainties
  • Raising to a Power: Multiply percentage uncertainty by power
• How do you calculate the mean value of a set of measurements?

  Add all values and divide by count
• What is the first step in calculating percentage uncertainty?

  Calculate the mean value

  
• How do you calculate half the range for uncertainty?

  1/2 × (largest - smallest value)
• What is the formula for percentage uncertainty?

  Uncertainty / measured value × 100%

  
• What are the key points about absolute and percentage uncertainties?

  • Absolute uncertainties (Δ) have same units as quantity
  • Percentage uncertainties have no units
  • Uncertainty in constants like π is zero
• Will uncertainties in trigonometric and logarithmic functions be tested in the exam?

  No, they will not be tested