Understanding Metric System Prefixes

Sep 23, 2024

Metric System Prefixes Lecture Notes

Overview

  • Discussion on the prefixes of the metric system, their symbols, and associated multipliers.
  • Importance of understanding and using conversion factors for solving problems.

Common Metric Prefixes

Positive Multipliers

  1. Deca (da)
    • Multiplier: 10 (10^1)
  2. Hecto (h)
    • Multiplier: 100 (10^2)
  3. Kilo (k)
    • Multiplier: 1,000 (10^3)
    • Example: 1 kilogram = 1,000 grams
  4. Mega (M)
    • Multiplier: 1,000,000 (10^6)
    • Example: 1 megawatt = 1,000,000 watts
  5. Giga (G)
    • Multiplier: 1,000,000,000 (10^9)
    • Example: 1 gigajoule = 1,000,000,000 joules
  6. Tera (T)
    • Multiplier: 1,000,000,000,000 (10^12)
    • Example: 1 terawatt = 1,000,000,000,000 watts

Higher Multipliers (Less Common)

  • Peta (P): 10^15 (quadrillion)
  • Exa (E): 10^18 (quintillion)
  • Zeta (Z): 10^21 (sextillion)
  • Yoda (Y): 10^24 (septillion)

Negative Multipliers

  1. Deci (d)
    • Multiplier: 0.1 (10^-1)
  2. Centi (c)
    • Multiplier: 0.01 (10^-2)
  3. Milli (m)
    • Multiplier: 0.001 (10^-3)
  4. Micro (µ)
    • Multiplier: 0.000001 (10^-6)
  5. Nano (n)
    • Multiplier: 0.000000001 (10^-9)
  6. Pico (p)
    • Multiplier: 0.000000000001 (10^-12)

Lower Multipliers (Less Common)

  • Femto (f): 10^-15
  • Atto (a): 10^-18
  • Zepto (z): 10^-21
  • Yocto (y): 10^-24

Conversion Factor Guidelines

  • Always attach a 1 to the prefix.
  • Attach the multiplier to the base unit (e.g., grams, meters, joules).
  • Write conversion factors consistently to ease unit conversion tasks.

Example Conversion Problems

One-Step Conversion

  • Example: Converting 478 meters to kilometers
    • Conversion factor: 1 km = 1,000 meters
    • Calculation: 478 m * (1 km / 1,000 m) = 0.478 km

Two-Step Conversion

  • Example: Converting 496 picometers to micrometers
    • Step 1: Picometer to Meter
      • 1 picometer = 1 * 10^-12 meters
    • Step 2: Meter to Micrometer
      • 1 micrometer = 1 * 10^-6 meters
    • Result: Convert using multiplication of conversion factors

Tips for Conversion

  • When using conversion factors, arrange fractions to cancel out the original unit and introduce the desired unit.
  • Use scientific notation for clarity and consistency in answers.
  • Practice with additional resources for more complex problems.

Note: For more complex examples, search for unit conversion videos by the "Organic Chemistry Tutor" on YouTube.