Lecture on Unit Conversion via Dimensional Analysis

Overview

• Dimensional Analysis: Also known as the factor label method or unit factor method.
• Purpose: A powerful problem-solving technique for converting between units.

Example Problem: Converting Pounds to Kilograms

• Problem: Convert 495 pounds to kilograms.
• Conversion Factor: 1 kilogram = 2.2 pounds.

Steps:

1. Write Down Quantity: Start with 495 pounds.
2. Multiply by a Fraction:
   • Use the conversion factor.
   • Place 2.2 pounds (from conversion factor) in the denominator.
   • Place 1 kilogram in the numerator.
3. Cancel Units:
   • Pounds cancel out, leaving kilograms.
4. Calculate:
   • Perform division: 495 / 2.2 = 225 kg.
   • Note: The fraction equals 1 since 1 kg = 2.2 pounds.

Example Problem: Converting Kilograms to Tons

• Problem: Convert 1920 kilograms to tons.
• Required Conversion Factors:
  1. Kilograms to Pounds: 1 kg = 2.2 pounds.
  2. Pounds to Tons: 2000 pounds = 1 ton.

Steps:

Two-Step Conversion:

1. Convert Kilograms to Pounds:
   • Start with 1920 kilograms.
   • Multiply by fraction with 1 kg in the denominator and 2.2 pounds in the numerator.
   • Calculate: 1920 * 2.2 = 4224 pounds.
2. Convert Pounds to Tons:
   • Start with 4224 pounds.
   • Multiply by fraction with 2000 pounds in the denominator and 1 ton in the numerator.
   • Calculate: 4224 / 2000 = 2.11 tons.*

Single-Step Conversion:

• Combine conversion steps into one.
• Process:
  • Begin with 1920 kilograms.
  • Multiply by the first conversion factor (2.2 pounds / 1 kg).
  • Multiply by the second conversion factor (1 ton / 2000 pounds).
  • Perform calculations from left to right: Multiply when 1 is in the denominator, divide when 1 is in the numerator.
  • Final Calculation: (1920 * 2.2) / 2000 = 2.11 tons.*

Conclusion

• Efficiency: Using conversion factor fractions helps simplify calculations, allowing multiple conversions in one step.
• Benefit: This method outlines when to multiply or divide based on unit placement, ensuring consistent accuracy.

Additional Resources

• Visit ketzbook.com for more examples and tutorials.
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