• 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