Unit Conversion Using Conversion Factors

Introduction

• Learn how to convert units using conversion factors.
• Also known as dimensional analysis or the factor label method.
• Goal: Simplify unit conversion to make it easy.

Example 1: Converting Pounds to Grams

Problem Statement

• Convert 3.45 pounds to grams.

Steps

1. Identify Conversion Relationship
   • 1 pound = 453.6 grams.
   • This can be found through various resources like textbooks or online.
2. Create Conversion Factors
   • Can write two conversion factors from the relationship:
     • ( \frac{1 \text{ pound}}{453.6 \text{ grams}} )
     • ( \frac{453.6 \text{ grams}}{1 \text{ pound}} )
3. Choose the Correct Conversion Factor
   • Choose the factor that cancels the initial unit (pounds) and leaves the desired unit (grams).
   • Here, use ( \frac{453.6 \text{ grams}}{1 \text{ pound}} ) because pounds cancel out.
4. Perform Calculation
   • Calculation: ( 3.45 \times 453.6 \text{ grams} )
   • Result: 1,560 grams.

Key Takeaways

• Ignore significant figures in basic conversions.
• Focus on understanding unit cancellation first.

Example 2: Converting Feet to Miles

Problem Statement

• Convert 15,100 feet to miles.

Steps

1. Identify Conversion Relationship
   • 1 mile = 5,280 feet.
2. Create Conversion Factors
   • ( \frac{1 \text{ mile}}{5,280 \text{ feet}} )
   • ( \frac{5,280 \text{ feet}}{1 \text{ mile}} )
3. Choose the Correct Conversion Factor
   • Use ( \frac{1 \text{ mile}}{5,280 \text{ feet}} ) to cancel feet.
4. Perform Calculation
   • Calculation: ( 15,100 \times \frac{1}{5,280} )
   • Result: 2.86 miles.

Example 3: Converting Euros to US Dollars

Problem Statement

• Convert 125 euros to US dollars given exchange rate: 1 USD = 0.78 euros.

Steps

1. Use Given Conversion Relationship
2. Choose the Correct Conversion Factor
   • Use ( \frac{1 \text{ USD}}{0.78 \text{ euros}} ) to cancel euros.
3. Perform Calculation
   • Calculation: ( 125 \times \frac{1}{0.78} )
   • Result: 160 USD.

Example 4: Converting Milliliters to Liters

Problem Statement

• Convert 23,500 milliliters to liters.

Steps

1. Identify Conversion Relationship
   • 1 liter = 1,000 milliliters.
2. Choose the Correct Conversion Factor
   • Use ( \frac{1 \text{ liter}}{1,000 \text{ milliliters}} ) to cancel milliliters.
3. Perform Calculation
   • Calculation: ( 23,500 \times \frac{1}{1,000} )
   • Result: 23.5 liters.

Conclusion

• Conversion factors enable easy switching between units by canceling units appropriately.
• Future topics include multi-step conversion and understanding the rationale behind conversion factor setups.