Convert from pie [Texas] to gnat's eye

Unit Definition (pie [Texas])
The pie is a traditional foot of Spain. The pie equals 1/3 vara or 12 pulgadas. In Texas, 1/3 vara is 11 1/9 inches or 28.22 centimeters.

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).