Learn Unit Conversion the Easy Way

Introduction

• Method: Dimensional Analysis (also known as Factor-Label Method or Unit-Factor Method)
• Versatile and powerful problem-solving technique

Simple Unit Conversion Example

• Problem: Convert 495 lbs to kilograms
• Conversion Factor: 1 kg = 2.2 lbs

Steps:

1. Write Quantity:
   • Start with the quantity to convert: 495 lbs
2. Multiply by Fraction:
   • Use the conversion factor in fraction form
   • Arrange 2.2 lbs on the bottom and 1 kg on the top
3. Cancel Units:
   • Pounds cancel out, leaving kilograms
4. Calculate:
   • Perform division: 495 ÷ 2.2 = 225 kg

Key Point:

• The fraction used equals 1 (1 kg = 2.2 lbs)

Complex Unit Conversion Example

• Problem: Convert 1920 kg to tons
• Conversion Factors:
  • 1 kg = 2.2 lbs (for kg to lbs)
  • 1 ton = 2000 lbs (for lbs to tons)

Steps:

1. Initial Conversion (kg to lbs):
   • Quantity: 1920 kg
   • Fraction: 1 kg (bottom), 2.2 lbs (top)
   • Calculate: 1920 × 2.2 = 4224 lbs
2. Final Conversion (lbs to tons):
   • Quantity: 4224 lbs
   • Fraction: 2000 lbs (bottom), 1 ton (top)
   • Calculate: 4224 ÷ 2000 = 2.11 tons

Important Note:

• Round to 3 significant figures due to initial measurement (1920 kg)

Combined Steps Approach

• Efficiency: Combine all conversion factors into one step
• Procedure:
  • Multiply by sequential conversion factor fractions
  • Cancel out units step by step
  • Calculation sequence: Multiply when 1 is on the bottom, divide when 1 is on top

Example:

• Start with 1920 kg
• Conversion: 1 kg (bottom), 2.2 lbs (top); then 2000 lbs (bottom), 1 ton (top)
• Calculate: 1920 × 2.2 ÷ 2000 = 2.11 tons

Conclusion

• Dimensional analysis is a powerful method for unit conversion
• Helps determine when to multiply or divide based on unit cancellation

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