Convert from button measure to hair's breadth

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.

Unit Definition (hair's breadth)
The hair's breadth is a common informal unit of distance. Human hairs vary considerably in width, depending on age, color, genetics, and other factors. An average hair is approximately 70 to 100 micrometers (µm) in diameter, so, as a rough standard, a hair's breadth is 100 µm or 0.1 millimeter (mm).