Metric System Prefixes and Conversion Factors

Metric Prefixes and Symbols

• Deca (da)
  • Multiplier: $10^1$ or 10
• Hecto (h)
  • Multiplier: $10^2$ or 100
• Kilo (k)
  • Multiplier: $10^3$ or 1,000
  • Example: 1 kilogram = 1,000 grams
• Mega (M)
  • Multiplier: $10^6$ or 1,000,000
  • Example: 1 megawatt = 1,000,000 watts
• Giga (G)
  • Multiplier: $10^9$ or 1,000,000,000
  • Example: 1 gigajoule = 1,000,000,000 joules
• Tera (T)
  • Multiplier: $10^{12}$ or 1,000,000,000,000
  • Example: 1 terawatt = 1,000,000,000,000 watts
• Peta (P)
  • Multiplier: $10^{15}$ or 1,000,000,000,000,000
• Exa (E)
  • Multiplier: $10^{18}$ or 1,000,000,000,000,000,000
• Zetta (Z)
  • Multiplier: $10^{21}$ or 1 sextillion
• Yotta (Y)
  • Multiplier: $10^{24}$ or 1 septillion

Negative Exponent Prefixes

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

Important Conversion Technique

• Attach a '1' to the prefix
• Multiply the base unit by the multiplier
• Write conversion factors with these rules for easy unit conversions

Example Conversion Problems

Conversion: Meters to Kilometers

• Given: 478 meters
• Conversion Factor: 1 kilometer = $1 \times 10^3$ meters
• Calculation: $\frac{478}{1,000} = 0.478$ kilometers

Conversion: Liters to Milliliters

• Given: 0.236 liters
• Conversion Factor: 1 milliliter = $1 \times 10^{-3}$ liters
• Calculation: $0.236 \times 1,000 = 236$ milliliters

Conversion: Picometers to Micrometers

• Given: 496 picometers
• Conversion Factors:
  • 1 picometer = $1 \times 10^{-12}$ meters
  • 1 micrometer = $1 \times 10^{-6}$ meters
• Calculation:
  • Convert picometers to meters, then meters to micrometers
  • Using scientific notation adjustments: $4.96 \times 10^{-4}$ micrometers

Conversion: Nanometers to Kilometers

• Given: $3.54 \times 10^7$ nanometers
• Conversion Factors:
  • 1 nanometer = $1 \times 10^{-9}$ meters
  • 1 kilometer = $1 \times 10^3$ meters
• Calculation: $3.54 \times 10^{-5}$ kilometers

Tips for Converting Units

• Cross out units to check conversion steps
• Use scientific notation for clarity and accuracy
• Move exponents between numerator and denominator to change signs
• Add exponents when multiplying common bases