1.1.3 Homogeneity of Physical Equations & Powers of Ten

• An important skill is to be able to check the homogeneity of physical equations using the SI base units
• The units on either side of the equation should be the same
• To check the homogeneity of physical equations:
  • Check the units on both sides of an equation
  • Determine if they are equal
  • If they do not match, the equation will need to be adjusted

How to check the homogeneity of physical equations

• 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 (1000000000000000000000 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