Convert from fathom [ancient] to gnat's eye

Unit Definition (fathom [ancient])
A fathom is a unit of measure equal to 2 yards or 6 feet, or 1.8288 metres. The name of the unit derives from the Old English word fæthm meaning 'outstretched arms' which was the original definition of the unit's measure.

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).