Error & Uncertainty

• What is an absolute number in counting?

  A count of how many there are
• How is mass described when measured?

  It may be said to be an approximation
• When might results be provided with less significant figures?

  When a very specific value is not required
• What does the decimal show in a value?

  The magnitude of a value
• Are zeros before a number part of significant figures?

  No, they are not part of significant figures
• Are zeros within a number part of significant figures?

  Yes, they are part of significant figures
• Why are significant figures important?

  They indicate the accuracy of a result
• Can an answer be accurate to more significant figures than the original components?

  No, it cannot
• What should be considered at the end of a calculation?

  All information and significant figures
• How is BMI calculated?

  BMI = weight (kg) / (height x height) (m²)
• What is the BMI if weight is 75 kg and height is 1.72 m?

  BMI = 25.351541
• How should BMI be quoted?

  To 2 significant figures
• What is the BMI if calculated using 1.7 m for height?

  BMI = 26
• How do significant figures differ from decimal places?

  Significant figures measure precision, decimal places do not
• What must your answer contain when using a calculator?

  The same degree of precision as the factors
• How does subtraction affect significant figures?

  The answer has fewer significant figures than the inputs
• In multiplication and division, what is more important?

  The number of significant figures
• How is the answer reported in multiplication and division?

  To the same level of significant figures as the lowest number
• What is the relevance of significant figures in pharmacy?

  They are crucial for accurate measurements
• What are random errors?

  Errors with equal chance of being +ve or -ve
• What can reduce systematic errors?

  Proper calibration of instruments
• What defines accurate measurements?

  Values close to the true value
• What defines precise measurements?

  They are repeatable
• What is the rough rule for estimating errors?

  Uncertainty = range / 2
• How should errors be quoted?

  Corresponding to a single significant figure error
• What does the range method provide?

  A worst-case scenario for uncertainty
• How is overall error calculated?

  Using Pythagoras’ theorem
• What does the mathematical method of uncertainty involve?

  Propagation of uncertainty
• What is the formula for overall error?

  Overall error = \sqrt{(error B)^2 + (error C)^2}
• How should errors be written?

  To one significant figure
• How do you express fractional errors as percentage errors?

  Percentage uncertainty = $\frac{b}{B} \times 100$
• How do you calculate error in multiplication?

  Using fractional uncertainties
• What is the formula for fractional error in multiplication?

  Fractional error = \sqrt{(F.E. B)^2 + (F.E. C)^2}
• What is the BMI if mass is 63 kg and height squared is 2.96 m²?

  BMI = 21.28378
• How is the associated error calculated for BMI?

  By combining fractional uncertainties
• What is the final BMI value with associated error?

  BMI = 21.28 ± 0.08