Expert: Josh - 4/1/2008

Question
the following procedure converts 8 ft to inches
8ft=8ft(1)
  =8ft(12in)
        1
  =96 inches
explain the substitution that took place.


Answer
Lopaka,

I am not sure that the question reads right. I think this is how it should go:

8 ft = 8 [ft] x (12[in]/1[ft])

Note: We have introduced the term (12[in]/1[ft]). The fraction inside the round brackets reads twelve inches per feet. Although this identity, i.e., "12/1 [in/ft]", does not alter the nature of the equation, i.e., everything holds true when we make the substitution, this multiplication enables us to convert the units from "ft" to "in". So, how does it work? Basically, the units [ft]/[ft] cancel out, giving us a dimensionless quantity. Thus, the unit remaining on the right hand side of the equation becomes effectively [in].

The second line should read:
   = 96 [in]