Convert from mile [international] to button measure

Unit Definition (mile [international])
The mile is one of the most common measurements of distance. It originates from the Latin word for 1000, 'mille'. Originally a mile was the distance a Roman legion could march in 1000 paces. In medieval Britain, several mile units were used, including the modern mile defined as 8 furlongs (1609 meters). Note that French, Scottish and Irish miles varied from the English. In 1592, Parliament defined the statute mile to be 8 furlongs or 1609.344 meters.

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.