Key Concepts: Measurement Uncertainty & Error Analysis

Types of Errors

• Systematic Errors: Consistent, repeatable errors that shift all measurements in the same direction. Caused by faulty equipment, calibration issues, or flawed technique. They affect accuracy.
• Random Errors: Unpredictable fluctuations that cause measurements to scatter around the true value. Caused by limitations of the instrument or observer. They affect precision.

Expressing Uncertainty

• Absolute Uncertainty: The ± range of a measurement. E.g., 5.0 ± 0.1 cm.
• Percentage Uncertainty: (absolute uncertainty / measured value) × 100%. E.g., (0.1/5.0) × 100% = 2%.

Propagation of Uncertainties

• Addition/Subtraction: Add absolute uncertainties. If A = 5.0 ± 0.1 and B = 3.0 ± 0.2, then A + B = 8.0 ± 0.3.
• Multiplication/Division: Add percentage uncertainties.
• Powers: Multiply the percentage uncertainty by the power. If x has 2% uncertainty, x³ has 6% uncertainty.