Overview
This lecture explains how to convert between units of the same type using conversion factors, with a focus on exactness, significant figures, and step-by-step examples.
The Concept of Conversion Factors
- Conversion factors are ratios that express the relationship between two equivalent units.
- Example: 1 yard = 3 feet can be used as 3 feet/1 yard or 1 yard/3 feet.
- When multiplying by a conversion factor, units you want to cancel should appear in opposite positions (numerator/denominator).
Applying Conversion Factors
- To convert units, multiply the initial quantity by the appropriate conversion factor so that unwanted units cancel out.
- Example: 3 yards × (3 feet / 1 yard) = 9 feet (yards cancel).
- The unit you want to end with should be in the numerator of the conversion factor.
Working with Metric Units
- 1 millimeter (mm) = 0.001 meter (m); 1,000 mm = 1 m.
- To convert meters to millimeters: multiply by 1,000.
- To convert millimeters to meters: divide by 1,000.
- Use scientific notation for clarity with significant figures, e.g., 5.5 m = 5.5 × 10³ mm.
Deciding Which Conversion Factor to Use
- Choose the conversion factor that cancels the original unit from your measurement.
- The starting unit is assumed to be in the numerator; place the same unit in the denominator of the conversion factor.
Additional Examples
- 35.9 kiloliters (kL) × (1,000 liters / 1 kL) = 35,900 liters (L).
- 67.08 microliters (μL) × (1 L / 1×10⁶ μL) = 6.708 × 10⁻⁵ L.
Significant Figures and Exact Numbers
- Conversion factors from defined equalities are exact and do not affect the significant figures of your answer.
- The number of significant figures in your answer should match the original measurement.
Key Terms & Definitions
- Conversion Factor — a ratio used to express how many of one unit equals another.
- Equality — a statement that two quantities are equivalent (e.g., 1 yard = 3 feet).
- Significant Figures (Sig Figs) — digits in a measurement that are known with certainty plus one estimated digit.
- Dimensional Analysis — another term for unit conversion using conversion factors.
- Exact Number — a value known with complete certainty, not limiting sig figs.
Action Items / Next Steps
- Practice single- and multi-step unit conversions.
- Review and memorize common unit equalities and SI prefixes.
- Prepare for problems involving dimensional analysis with different unit types.