Overview
This lecture covers writing equalities and conversion factors between units, distinguishing between exact and measured numbers, and practicing with examples common in chemistry.
Writing Equalities and Conversion Factors
- An equality shows two units are the same amount (e.g., 100 cm = 1 m).
- Conversion factors are fractions expressing the equality in both possible arrangements (e.g., 100 cm/1 m or 1 m/100 cm).
- The choice of conversion factor depends on which unit needs to be canceled in calculations.
Common Conversion Examples
- 100 cm = 1 m (metric: exact numbers).
- 1 km = 0.621 miles or 1 mile = 1.61 km (metric to US: measured numbers).
- 1 lb = 453.592 g (measured numbers).
- 1 qt = 0.946 L (measured numbers).
- 2.54 cm = 1 inch (measured number).
Exact vs. Measured Numbers and Significant Figures
- Numbers within the same measurement system (e.g., metric) are exact and have infinite significant figures.
- Numbers converting between systems are measured and have a limited number of significant figures.
- Only measured numbers count in significant figure calculations.
Practice Problems and Applications
- To write an equality: state both units as equal (e.g., 1 L = 1.06 qt).
- To write conversion factors: arrange the equality as fractions in either direction.
- Identify if each number in a conversion is exact (unlimited sig figs) or measured (limited sig figs).
- Medication examples: 2.5 mg/tablet, 10 mg/tablet, 1.5 g/mL—all can be written as equalities and conversion factors in both directions.
Key Terms & Definitions
- Equality — Statement showing two different units are the same quantity (e.g., 100 cm = 1 m).
- Conversion Factor — A ratio or fraction derived from an equality, used to convert between units.
- Exact Number — Number known with complete certainty, typically within a measurement system, with infinite significant figures.
- Measured Number — Number based on measurement, limited by instrument precision, with a finite number of significant figures.
- Significant Figures (Sig Figs) — The digits in a number that carry meaning for its precision.
Action Items / Next Steps
- Memorize common multiplicative prefixes (e.g., centi-, kilo-) and their relationships.
- Download and keep the provided reference sheet for conversion factors and equations.
- Practice identifying exact and measured numbers in conversion problems.
- Work through textbook problems in section 2.46, 2.48, and 2.54.