Errors, Uncertainty, and Significant Figures
Learning Objectives
- Students will be able to calculate absolute and relative errors
- Students will be able to apply rules of significant figures in calculations
- Students will understand experimental uncertainty and how to express it
Core Concepts
- Absolute error and relative error calculations
- Rules for significant figures in measurements and calculations
- Expressing uncertainty: measurement ± uncertainty
Formulas
$$\varepsilon_{abs} = |x_{meas} - x_{acc}|$$
Difference between measured and true value in the same units
$$\varepsilon_{rel} = \frac{\varepsilon_{abs}}{x_{acc}} \times 100\%$$
Percentage difference, useful for comparing errors of different magnitudes
Interesting Fact
The uncertainty principle in quantum mechanics sets fundamental limits on how precisely we can know certain properties
Key Scientist
Werner Heisenberg
Formulated the uncertainty principle in quantum mechanics
Ancient Wisdom
The uncertainty principle validates ancient philosophical views that complete knowledge of reality may be fundamentally impossible, echoing Zen paradoxes.
Want to truly master this? Try the interactive lesson!
Start Lesson