Metric System Prefixes and Conversion

Introduction

• Discussion on metric system prefixes, symbols, and multipliers
• Emphasis on conversion factors and their application in problem-solving

Metric System Prefixes and Symbols

Positive Exponents

• Deca
  • Symbol: da
  • Multiplier: (10^1) or 10
• Hecto
  • Symbol: h
  • Multiplier: (10^2) or 100
• Kilo
  • Symbol: k
  • Multiplier: (10^3) or 1,000
• Mega
  • Symbol: M
  • Multiplier: (10^6) or 1,000,000
• Giga
  • Symbol: G
  • Multiplier: (10^9) or 1,000,000,000
• Tera
  • Symbol: T
  • Multiplier: (10^{12}) or 1,000,000,000,000
• Peta
  • Symbol: P
  • Multiplier: (10^{15}) or 1,000,000,000,000,000
• Exa
  • Symbol: E
  • Multiplier: (10^{18})
• Zetta
  • Symbol: Z
  • Multiplier: (10^{21})
• Yotta
  • Symbol: Y
  • Multiplier: (10^{24})

Negative Exponents

• Deci
  • Symbol: d
  • Multiplier: (10^{-1})
• Centi
  • Symbol: c
  • Multiplier: (10^{-2})
• Milli
  • Symbol: m
  • Multiplier: (10^{-3})
• Micro
  • Symbol: µ
  • Multiplier: (10^{-6})
• Nano
  • Symbol: n
  • Multiplier: (10^{-9})
• Pico
  • Symbol: p
  • Multiplier: (10^{-12})
• Femto
  • Symbol: f
  • Multiplier: (10^{-15})
• Atto
  • Symbol: a
  • Multiplier: (10^{-18})
• Zepto
  • Symbol: z
  • Multiplier: (10^{-21})
• Yocto
  • Symbol: y
  • Multiplier: (10^{-24})

Conversion Factors

• Attach "1" to the prefix and multiply by the base unit multiplier
• Helps in converting units from one form to another

Conversion Examples

One-Step Conversion

1. Example: Convert 478 meters to kilometers

   • Conversion factor: 1 km = (1 \times 10^3) meters
   • Process: (478 \text{ m} \div 1000 = 0.478 \text{ km})

2. Example: Convert 0.236 liters to milliliters

   • Conversion factor: 1 mL = (1 \times 10^{-3}) L
   • Process: (0.236 \text{ L} \times 1000 = 236 \text{ mL})

Two-Step Conversion

1. Example: Convert 496 picometers to micrometers

   • Step 1: Convert picometers to meters
     • Conversion: 1 pm = (1 \times 10^{-12}) m
   • Step 2: Convert meters to micrometers
     • Conversion: 1 µm = (1 \times 10^{-6}) m
   • Process involves moving exponents and simplifying
     • Final: (4.96 \times 10^{-4}) micrometers

2. Example: Convert (3.54 \times 10^7) nanometers to kilometers

   • Step 1: Convert nanometers to meters
     • Conversion: 1 nm = (1 \times 10^{-9}) m
   • Step 2: Convert meters to kilometers
     • Conversion: 1 km = (1 \times 10^3) m
   • Result: (3.54 \times 10^{-5}) km

Tips for Conversion

• Always attach "1" to the prefix and the multiplier to the base unit
• Use scientific notation and follow exponent rules for simplification
• Common conversions involve writing the conversion factor first and then applying it through fractions

Additional Resources

• For more practice, search "unit conversion organic chemistry tutor" on YouTube for advanced problems.