Overview
This lecture explains how to perform unit conversions using dimensional analysis (factor-label method), including single and multi-step conversions with practical examples.
Dimensional Analysis Basics
- Dimensional analysis (factor-label method) is used to convert between units using conversion factors.
- Always start by writing down the quantity to convert, including its units.
- Multiply the initial value by a fraction (conversion factor) so that unwanted units cancel.
- Place the unit you want to cancel in the denominator and the new unit in the numerator.
- The conversion factor fraction always equals one because both numerator and denominator represent the same quantity.
Example: Pounds to Kilograms
- Example: Convert 495 lbs to kilograms using the conversion factor 1 kg = 2.2 lbs.
- Set up the conversion: (495,\text{lbs} \times \frac{1,\text{kg}}{2.2,\text{lbs}}).
- Units of pounds cancel, leaving kilograms.
- Calculate: (495 \div 2.2 = 225,\text{kg}).
- The conversion factor fraction equals one, validating the process.
Multi-Step Conversion: Kilograms to Tons
- Some conversions require multiple steps and factors (e.g., kg to lbs to tons).
- Example: Convert 1920 kg to tons using 1 kg = 2.2 lbs and 1 ton = 2000 lbs.
- Step 1: (1920,\text{kg} \times \frac{2.2,\text{lbs}}{1,\text{kg}} = 4224,\text{lbs}).
- Step 2: (4224,\text{lbs} \times \frac{1,\text{ton}}{2000,\text{lbs}} = 2.11,\text{tons}).
- Always arrange conversion factors to cancel the preceding unit.
Combining Conversion Steps
- Multiple conversions can be combined: (1920,\text{kg} \times \frac{2.2,\text{lbs}}{1,\text{kg}} \times \frac{1,\text{ton}}{2000,\text{lbs}}).
- Cancel units across all factors and compute: (1920 \times 2.2 \div 2000 = 2.11,\text{tons}).
- Multiplying or dividing depends on whether the "1" is in the denominator or numerator.
Key Terms & Definitions
- Dimensional Analysis — A method for converting units using multiplication by conversion factors.
- Conversion Factor — A fraction representing equivalent values in different units (e.g., (1,\text{kg} = 2.2,\text{lbs})).
- Significant Figures — The number of meaningful digits in a number, which determines result precision.
Action Items / Next Steps
- Practice unit conversion problems using the factor-label method.
- Identify conversion factors for common units.
- Pay attention to significant figures in final answers.