Convert from gnat's eye to pouce

Unit Definition (gnat's eye)
The gnat's eye is an idiomatic "unit" of distance; it's common to hear that something is "as small as a gnat's eye". In fact, the eyes of typical gnats tend to have diameters similar in size to a hair's breadth: roughly 100-150 micrometers (0.10-0.15 millimeters).

Unit Definition (pouce)
The pouce is a French "inch" unit, equal to 1/12 pied. Based on the pied de roi, the pouce equals about 1.066 inches or 2.707 centimeters. The word pouce means "thumb" in French.