this post was submitted on 09 Sep 2025
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Because there's a extra system of measurement change hiding in the middle. The Inches, Feet and Yards system (with the familiar 12:1 and 3:1 ratios we know and love), and Rods, Chains, Furlongs and Miles system. Their conversation rates are generally "nice", with ratios of 4 rods : 1 chain, 10 chains : 1 furlong, and 8 furlongs : 1 mile.
So where do we get 5,280 with prime factors of 2^5, 3, 5 and 11? Because a chain is 22 yards long. Why? Because somewhere along the line, inches, feet and yards went to a smaller standard, and the nice round 5 yards per rods became 5 and 1/2 yards per rod. Instead of a mile containing 4,800 feet (with quarters, twelfths and hundredths of miles all being nice round numbers of feet), it contained an extra 480 feet that were 1/11th smaller than the old feet.
The fun one is a nautical mile. Which is 6076.12 feet. How'd we get there? A nautical mile is equal to a minute of latitude, which happens to be just a bit bigger but on the order of magnitude of most "miles" to include the US statute mile.