Convert from Q to gnat's eye

Unit Definition (Q)
The Q is a metric unit of distance equal to exactly 0.25 millimeter (9.8425 mils) used by typographers and page designers in Japan, in Germany, and in other countries in preference to the traditional point. One Q is equal to about 0.71 point, a little more or less depending on the exact definition of the point. This unit is also spelled kyu.

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).