Convert from hair's breadth to douzieme [watchmaking]

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).

Unit Definition (douzieme [watchmaking])
The douzieme is a traditional unit of distance used in watchmaking. The word is French for "twelfth," and a douzième is equal to 1/12 Swiss ligne. This is about 188 micrometers (microns) or 7.4 mils.