Lecture on Unit Conversions

Importance and Agenda

• Importance of Conversions: Essential for STEM courses and future applications.
• Lecture Focus: Simple conversions, dimensional analysis.

Conversion Basics

• Example: Converting days to seconds.
  • Understand the Question: Convert 5 days into seconds.
  • Steps:
    1. Know the equivalency statements:
       • 1 day = 24 hours
       • 1 hour = 60 minutes
       • 1 minute = 60 seconds
    2. Create conversion factors:
       • 1 day = 24 hours or 24 hours = 1 day
       • 1 hour = 60 minutes, 60 minutes = 1 hour
       • 1 minute = 60 seconds, 60 seconds = 1 minute

Dimensional Analysis

• Process:
  • Start with the given unit.
  • Use conversion factors to switch units, canceling out the previous unit.
  • Example: Convert 5 days to seconds.
    • Calculation: 5 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 432,000 seconds.*

Significant Figures (Sig Figs)

• Definition: Importance in reporting measurements and calculations.
• Example: 5.0 days = 2 significant figures.
• Defined Values:
  • Defined conversions (e.g., 60 minutes = 1 hour) have infinite significant figures.
• Scientific Notation:
  • Purpose: Used to manage large numbers and maintain sig figs.
  • Example: 432,000 seconds becomes 4.3 x 10^5 seconds with 2 sig figs.

Examples and Practice Problems

Example 1: Grading Lab Reports

• Problem: Alex can grade 5.5 lab reports per hour; with 52 students, how long will grading take?
• Conversion Factors:
  • 1 hour = 5.5 lab reports
  • 52 lab reports for 52 students
• Calculation: 52 lab reports / (5.5 lab reports/hour) = 9.5 hours

Example 2: Big Mac Consumption

• Problem: Slip and Jimmy eats 2 Big Mac meals/day; with $118,229, how long can he eat?
• Conversion Factors:
  • 1 Big Mac meal = $15.78
  • 1 day = 2 Big Mac meals
• Steps:
  • Start with total money.
  • Convert money to Big Mac meals to days.
  • Result: Use calculated hours or days for the answer.

Example 3: Walking Distance

• Problem: Calculate distance Sally can walk in 7.3 minutes at 14 m/s.
• Conversion: Convert minutes to seconds, then use speed to find distance.
  • Steps:
    • 7.3 minutes * 60 seconds/minute * 14 meters/second.
    • Answer: 6.1 x 10^3 meters with 2 sig figs.

Closing Remarks

• Next Lecture: Transitioning to chapter 2.
• Recommendations: Practice more problems and focus on the application of conversion factors and significant figures.