My friend/coworker and I got into a pretty heated discussion about a label for a graph I had made and the units I was using. We work in internet advertising where there is a type of unit (I consider it a unit anyway) called a "CPM" (Cost Per Million, in dollars usually). To give some visualization to some data we're collecting, I made a line graph to see CPM over Time (seconds). I used CPM because the amount of money per second was too small to do in normal dollars.
My friend then saw the label for the graph, something like "CPM/Second", and the argument ensued. His claim was it could only be used as a rate and nothing else. Where he is getting confused (again, I think), is saying you are paying per million when you are only paying for one unit is sort of weird to think about. While knowing that it is often used as a rate, I also know it has been used as a unit and I don't see why that wouldn't make sense anyway.
My question is do humans interpret rates (Cost Per Milli, X Per Y, etc...) differently from absolute units? Are their any languages where this might be the case?