Lesson on Metric Conversions

Introduction to the Metric System

• Originated in Europe around 1800.
• Adopted worldwide as a standard system of measurement.
• Based on powers of ten.
• The U.S. is the only industrialized country not officially using the metric system.

Base Units and Prefixes

• Base Units: Meter (length), Liter (capacity), Gram (weight).
• Prefix System:
  • Kilo- (1000x the base unit): Kilometer, Kilogram, Kiloliter.
  • Milli- (1/1000x the base unit): Millimeter, Milliliter, Milligram.

Conversion Methods

• Using unit fractions to perform conversions.
• Verify using a table.

Example Conversions

Example 1: Grams to Milligrams

• Problem: Convert 4200 grams to milligrams.
• Process:
  • Write 4200 grams as a fraction (4200/1).
  • Use conversion: 1 gram = 1000 milligrams.
  • Form unit fraction: ( \frac{1000 \text{ mg}}{1 \text{ g}} ).
  • Simplify: ( 4200 \times 1000 = 4,200,000 \text{ mg} ).
• Verification:
  • Table conversion: Move decimal 3 places right.
  • Result: 4,200,000 mg.

Example 2: Centimeters to Meters

• Problem: Convert 45 centimeters to meters.
• Process:
  • Write 45 centimeters as a fraction (45/1).
  • Use conversion: 1 meter = 100 centimeters.
  • Form unit fraction: ( \frac{1 \text{ m}}{100 \text{ cm}} ).
  • Simplify: ( \frac{45}{100} = 0.45 \text{ m} ).
• Verification:
  • Table conversion: Move decimal 2 places left.
  • Result: 0.45 m.

Example 3: Milliliters to Kiloliters

• Problem: Convert 7,236,137 milliliters to kiloliters.
• Process:
  • Write as fraction (7,236,137/1).
  • Two-step conversion:
    1. 1 liter = 1000 milliliters, ( \frac{1 \text{ L}}{1000 \text{ ml}} ).
    2. 1 kiloliter = 1000 liters, ( \frac{1 \text{ kL}}{1000 \text{ L}} ).
  • Simplify: ( \frac{7,236,137}{1,000,000} = 7.236137 \text{ kL} ).
• Verification:
  • Table conversion: Move decimal 6 places left.
  • Result: 7.236137 kL.

Conclusion

• Both unit fractions and table methods yield the same conversion results.
• Important to understand and verify conversions through both methods.