Convert from rute [Germany] to gnat's eye

Unit Definition (rute [Germany])
The rute is a traditional German unit of distance corresponding to the English rod. In fact, "rute" is the German word for rod. The rute had varying lengths, as short as 10 fuss (German feet) and as long as 16 fuss. This could be anywhere from about 3 meters to 4.5 meters.

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).