Overview
This lecture covers unit conversion and dimensional analysis, using various examples to demonstrate the use of conversion factors and significant figures.
Introduction to Unit Conversion & Dimensional Analysis
- Unit conversion changes a quantity's measurement from one unit to another using conversion factors.
- Dimensional analysis involves multiplying by conversion factors to ensure correct units in calculations.
Conversion Factor Concept
- A conversion factor is a fraction equal to 1, used to convert between units without changing value.
- Conversion factors are arranged so unwanted units cancel out, leaving the desired unit.
Example Calculations
- To convert 8.7 inches to centimeters: multiply by (2.54 cm / 1 inch) to get 22 cm.
- To convert 15 cm to inches: multiply by (1 inch / 2.54 cm) to get 5.9 inches.
- To convert 0.2640 kg to grams: multiply by (1000 g / 1 kg) to get 264 g.
- To convert 0.354 L to microliters: multiply by (1 μL / 10⁻⁶ L) and use scientific notation for the answer.
- For multi-step conversions (e.g., miles to inches), chain relevant conversion factors: 2.5 mi × (5280 ft/1 mi) × (12 in/1 ft).
- To convert speed from km/h to m/s: 79.2 km/h × (1000 m/1 km) × (1 h/3600 s) = 22 m/s.
Handling Exponents & Powers in Units
- When converting squared or cubed units, raise the conversion factor to the same power (e.g., m² to cm²).
- Example: 0.951 m² to cm², use (1 cm / 10⁻² m)².
Volume and Complex Conversions
- To convert L to ft³, use 1000 L = 1 m³ and (1 m = 3.28 ft)³ for the conversion chain.
- Example: 1.2 L × (1 m³/1000 L) × (3.28 ft/1 m)³ = 0.042 ft³.
Time Unit Conversion Example
- To convert 6.57 × 10⁶ minutes to years: multiply by (1 h/60 min) × (1 day/24 h) × (1 yr/365 days).
- Final answer: 12.5 years.
Significant Figures in Conversions
- Exact numbers in conversion factors (e.g., 2.54 cm in 1 inch, 1000 g in 1 kg) are not counted for significant figures.
- Final answer’s significant figures should match the measured value, not the conversion factor.
Key Terms & Definitions
- Conversion Factor — A ratio (fraction) relating two units, equal to one, used for converting units.
- Significant Figures — Digits in a number that carry meaning for precision in measurements.
- Dimensional Analysis — A method for converting units using conversion factors to ensure correct units.
Action Items / Next Steps
- Practice converting between different units using dimensional analysis.
- Review significant figure rules for calculations involving measurements.
- Complete assigned homework problems on unit conversions and dimensional analysis.