Convert from pouce to gnat's eye

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.

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).