Overview
This lecture explains how to convert compound units (units involving multiple measurements) step-by-step, specifically with an example including grams, centimeters cubed, and seconds squared.
Steps to Convert Compound Units
- A compound unit involves more than one type of measurement, e.g., g·cm³/s².
- Convert each unit in the compound unit one at a time.
- Start by writing down the initial value and its units.
- Convert the mass unit: 1 kilogram (kg) = 1000 grams (g).
- Cancel out grams after conversion; the mass is now in kilograms.
- Convert the length unit: 1 meter (m) = 100 centimeters (cm).
- When converting cm³ to m³, cube both the number and the unit: (100 cm)³ = 1 m³, so 1 m³ = 1,000,000 cm³.
- Cancel out cm³ after conversion; the length is now in m³.
- Convert time units: 1 minute = 60 seconds and 1 hour = 60 minutes.
- For squared units, square the conversion factors: (60 s)² = 1 min², (60 min)² = 1 h².
- Cancel out seconds², then minutes²; time is now in hours².
- Multiply or divide by each conversion factor, depending on numerator or denominator positions.
- Adjust the final value according to significant figures in the original number.
Example Calculation
- Starting value: 25.3 g·cm³/s².
- Conversion sequence: grams to kilograms, cm³ to m³, s² to h², using appropriate powers for each conversion.
- Final calculation: 25.3 ÷ 1000 ÷ 100³ × 60² × 60² = 0.328 kg·m³/h² (rounded to three significant figures).
Key Terms & Definitions
- Compound unit — A measurement unit made from more than one basic unit (e.g., kg·m³/h²).
- Conversion factor — A numerical ratio used to change one unit to another.
- Significant figures — Digits in a measurement that contribute to its accuracy.
- Numerator/denominator — Top/bottom of a fraction; affects whether to multiply or divide during conversion.
Action Items / Next Steps
- Practice converting compound units with different combinations.
- Review rules for significant figures.
- Complete any assigned homework on unit conversions.