1.1.2 Powers of Ten

• Physical quantities can span a huge range of values
• For example, the diameter of an atom is about 10^–10 m (0.0000000001 m), whereas the width of a galaxy may be about 10²¹ m (1,000,000,000,000,000,000,000 m)
  • This is a difference of 31 powers of ten

• Powers of ten are numbers that can be achieved by multiplying 10 times itself
• It is useful to know the prefixes for certain powers of ten

Powers of Ten Table

Examples

• 5 kN = 5 kilonewtons= 5 × 10³ N (5000 N)
• 7 nC = 7 nanocoulombs = 7 × 10^-9 C (0.000000007 C)

J & eV

• A common unit conversion in physics is between Joules (J) and electronvolts (eV)
• The electronvolt is derived from the equation work done (or energy transferred) W = qV
  • 1 eV = 1.6 × 10^–19 C × 1 V = 1.6 × 10^–19 J

• To convert from J → eV, divide by 1.6 × 10^–19
• To convert from eV → J, multiply by 1.6 × 10^–19

J & kW h

• Another common unit conversion in physics is between Joules (J) and kilowatt-hours (kW h)
• To convert between J and kW h, expand the derived units and re-collect terms as follows:
  • 1 kW h = 3600 kW s (since 1 hour = 3600 s)
  • 3600 kW s = 3 600 000 W s (since 1 kW = 1000 W)
  • 3 600 000 W s = 3 600 000 J = 3.6 MJ (since power = energy / time or 1 W = 1 J s^–1)

• To convert from J → kW h, divide by 3.6 × 10⁶
• To convert from kW h → J, multiply by 3.6 × 10⁶

• To convert from J → eV, divide by 1.6 × 10^–19 J