5280 = 2^5 * 3 * 5 * 11, so the mile can be evenly divided in half many times like the gallon (quart, pint, cup, fluid ounce).
1 mile = 8 furlong = 1760 yard = 5280 feet = 63360 inch
1/2 mile = 4 furlong = 880 yard = 2640 feet = 31680 inch
1/4 mile = 2 furlong = 440 yard = 1320 feet = 15840 inch
1/8 mile = 1 furlong = 220 yard = 660 feet = 7920 inch
1/16 mile = 110 yard = 330 feet = 3960 inch
1/32 mile = 55 yard = 165 feet = 1980 inch
1/64 mile = 990 inch (82 ft 6 in)
1/128 mile = 495 inch (41 ft 3 in)
To continue the sequence, perhaps define a binary-inch (binch?) as 1/65536 mile ~= 0.9668 inch ~= 31/32 inch.
Tetrafurlong, bifurlong, furlong, semifurlong, demisemifurlong, hemidemisemifurlong.
But surveyors used 8 furlongs, 10 chains, 4 rod, 25 links = 7.92 inch.
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