Convert from fathom [ancient] to button measure

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 (button measure)
The button measure is a unit of distance equal to 1/40 inch (0.635 millimeter), used to measure the thickness of buttons.