Learn Unit Conversion the Easy Way

Method of Conversion

• Dimensional Analysis / Factor-Label Method / Unit-Factor Method
  • A versatile and powerful problem-solving technique.
  • The name doesn't matter, focus on the process.

Simple Unit Conversion Example

• Problem: Convert 495 lbs to kilograms.
• Conversion Factor: 1 kg = 2.2 lbs
• Steps:
  1. Write down the quantity to convert (495 lbs).
  2. Multiply by a fraction (conversion factor):
     • Write 2.2 lbs on the bottom (to cancel lbs).
     • Write 1 kg on the top (to convert to kg).
  3. Cancel out pounds, leaving kilograms.
  4. Calculate: 495 ÷ 2.2 = 225 kg
  5. The fraction 1 kg/2.2 lbs equals one because 1 kg = 2.2 lbs.

Complex Unit Conversion Example

• Problem: Convert 1920 kg to tons.
• Conversion Factors:
  • 1 kg = 2.2 lbs
  • 2000 lbs = 1 ton
• Two-Step Process:
  1. Convert kg to lbs:
     • Start with 1920 kg.
     • Multiply by the fraction where 1 kg is at the bottom and 2.2 lbs is at the top.
     • Result: 1920 × 2.2 = 4224 lbs.
  2. Convert lbs to tons:
     • Start with 4224 lbs.
     • Multiply by the fraction where 2000 lbs is at the bottom and 1 ton is at the top.
     • Calculate: 4224 ÷ 2000 = 2.11 tons.
  • Round to 3 significant figures because the initial figure (1920) has 3 significant figures.

Combined Conversion Method

• Process:
  • Combine steps by using multiple conversion factor fractions at once.
  • Start with the initial quantity and multiply by the first conversion factor.
  • Immediately multiply by the second conversion factor without solving the intermediate step:
    • Write conversion factors such that units cancel appropriately.
  • Calculate left to right, multiplying when '1' is on the bottom, dividing when '1' is on the top.
  • Example Calculation: 1920 × 2.2 ÷ 2000 = 2.11 tons.

Conclusion

• This method is powerful for multiple conversions.
• Conversion factors help determine when to multiply or divide.

Additional Info

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