What is a conversion factor?
a derived unit with a new name
the graph of recorded data
the density of a substance
a ratio of equivalent units

A ratio of equivalent units

Explanation:

A conversion factor is a ratio of equivalent units and depends on which units are to be converted.

For example we want to convert 275 [mm] to inches, so we have to find the right conversion factor to allow us to work that conversion.

275 [mm] = inches = ?

In this case the ratio is 1/25.4 = 0.039 [in/mm]

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form