Metric Conversions Lecture Notes

Understanding Conversion Factors

• Conversion Factor Definition: A conversion factor is a ratio used to convert one unit of measurement into another. Example: 1 dozen = 12.
• Real-life Examples: Minutes to seconds (1 minute = 60 seconds), hours to minutes, etc.

Metric System and Dimensional Analysis

• Metric Conversions: In science, metric conversions occur on an exponential scale (powers of 10).
• Dimensional Analysis: A method to convert units by multiplying with the appropriate conversion factor.
  • Example: Convert 345 meters to kilometers.
  • Conversion Factor: 1 kilometer = 1000 meters.

Metric Prefixes and Their Values

• Common Prefixes:
  • Kilo (k): 10³ or 1000
  • Hecto (h): 10² or 100
  • Deca (da): 10¹ or 10
  • Base Unit: 1
  • Deci (d): 10⁻¹ or 0.1
  • Centi (c): 10⁻² or 0.01
  • Milli (m): 10⁻³ or 0.001
  • Micro (μ): 10⁻⁶
  • Nano (n): 10⁻⁹
• Large vs. Small Units: Larger units have higher numerical values (powers of 10) and vice versa.

Example Problems

Problem 1: Converting Kiloliters to Milliliters

• Given: 0.5 kiloliters
• Conversion Steps:
  • Kiloliters to Liters: 1 kiloliter = 1000 liters
  • Liters to Milliliters: 1 liter = 1000 milliliters

Problem 2: Converting Pounds to Grams

• Given: 5 pounds
• Conversion Factor: 1 pound = 454 grams
• Steps:
  • Convert using the factor: 5 x 454 grams

Problem 3: Converting Meters to Inches

• Given: Meters
• Steps:
  • Meters to Centimeters: 1 meter = 100 centimeters
  • Centimeters to Inches: 2.54 centimeters = 1 inch

Problem 4: Speed Conversion

• Convert: 55 miles per hour to meters per second
• Steps:
  • Miles to Kilometers: 1 mile = 1.61 kilometers
  • Kilometers to Meters: 1 kilometer = 1000 meters
  • Hours to Minutes and then Seconds

Problem 5: Millimeters to Inches

• Given: 15 millimeters in 12 minutes
• Conversion:
  • Millimeters to Centimeters: 10 millimeters = 1 centimeter
  • Centimeters to Inches: 2.54 centimeters = 1 inch
• Time Conversion: Minutes to Hours

Key Tips for Dimensional Analysis

• Unit Placement: Place the unit to cancel on the opposite side of the fraction.
• Multiply or Divide: When crossing the line, multiply; when under the line, divide.
• Cubic Units: Cube the numbers when converting cubic units, except for known conversions like 1 milliliter = 1 centimeter cubed.

Practice and Queries

• Practice with provided examples and utilize discussion boards for any queries or additional help.