Overview
This lecture demonstrates how to use dimensional analysis to convert 365.0 picometers to feet using provided conversion factors.
Step-by-Step Conversion Process
- Start with the value to convert: 365.0 picometers (pm).
- Remember or look up that 1 meter (m) = 1 × 10¹² picometers.
- Convert picometers to meters by dividing by 1 × 10¹².
- Result after first step: 3.65 × 10⁻¹⁰ meters.
- Use the given conversion: 1 meter = 39.4 inches (in).
- Convert meters to inches by multiplying by 39.4.
- Result after second step: 1.438 × 10⁻⁸ inches.
- Use the given conversion: 12 inches = 1 foot (ft).
- Convert inches to feet by dividing by 12.
- Final result: 1.198 × 10⁻⁹ feet (rounded to 4 significant figures).
Converting Units: Key Steps
- Set up conversion factors so units cancel out step by step.
- Multiply by the top of the fraction, divide by anything on the bottom.
- Carefully track and cancel units at each step to avoid mistakes.
Significant Figures
- The original number (365.0) has 4 significant figures.
- The final answer should also be reported with 4 significant figures: 1.198 × 10⁻⁹ ft.
Key Terms & Definitions
- Dimensional Analysis — A method for converting between units using conversion factors.
- Picometer (pm) — A metric unit of length equal to 1 × 10⁻¹² meters.
- Significant Figures — The digits in a measurement that are meaningful in terms of accuracy.
Action Items / Next Steps
- Practice similar unit conversion problems using dimensional analysis.
- Review and memorize common metric conversion factors for future problems.