Ratio that compares two quantities in different units?

Answer 1

A ratio of two quantities that are measured using different measurement units is a third physical quantity that inherits the dimensions from the parents.

examples:

ratio between space s (meter) and time t (second) is velocity v=s/t measured in meters/second

ratio between energy E (Joule) and time t (seconds) is power (P) measured in Joules/second

ratio between heat Q (Joule) and Temperature T (°K) is entropy S=Q/T measured in Joule/°K

Different is the situation if we compare two measurements of the same time that are done in different measurement units. For example if we want to compare the distance between two cities measured in kilometers and the length of my bedroom measured in meters. In this case the result is an non dimensional ratio and to evaluate it the two measurements have to be converted in the same measurement unit. In the above example if the distance D between the cities is 100 km and the length of my bed room is L=8 meters the ratio has to be calculated as

D/L (all in meters) = 100*1000/8=12500.