Prefixes and Powers of Ten in Scientific Notation

1. Purpose of Prefixes

  • Express numbers in convenient powers of ten
  • Simplify standard form/scientific notation
  • Allow use of more appropriate units for scale

2. Key SI Prefixes

Large numbers:
  • Exa (E): 10^18
  • Peta (P): 10^15
  • Tera (T): 10^12
  • Giga (G): 10^9
  • Mega (M): 10^6
  • Kilo (k): 10^3
Small numbers:
  • Milli (m): 10^-3
  • Micro (μ): 10^-6
  • Nano (n): 10^-9
  • Pico (p): 10^-12
  • Femto (f): 10^-15
  • Atto (a): 10^-18

3. Examples of Usage

  • Time: 86,400 s = 8.64 x 10^4 s = 86.4 ks
  • Distance: 4.132 x 10^16 m = 41.32 Pm
  • Length: 4.0 x 10^-4 m = 40 mm
  • Mass: 1.0 x 10^-4 g = 100 mg

4. Volume Relationships

  • 1 L = 1 dm^3 = 1000 cm^3
  • 1 mL = 1 cm^3

5. Scientific Scale Examples

  • Sun'smass: 1.97 x 10^30 kg
  • Hydrogen atom radius: 5 x 10^-11 m
  • Earth's age: 1.433 x 10^17 s
  • Paper thickness: 1 x 10^5 nm = 1 x 10^-4 m
  • Pakistan power capacity: 4 x 10^4 MW
  • Hard disk capacity: 30 x 10^12 bytes

6. Key Points

  • Prefixes allow for more intuitive expression of very large or small quantities
  • Useful for converting between different scales and units
  • Essential in scientific and engineering communications