On a sectional chart legend, the airport icon with a solid magenta or blue disk is labeled as "Hard surfaced runways 1500 ft to 8069 ft in length". This seems like an extraordinarily arbitrary number to use as the upper limit before a different symbol is used. When I convert this to meters, or yards, or furlongs, or any other common unit, it doesn't correspond to any even number so it doesn't seem like a conversion from another system of units. What is the reason for this unusual dimension for a runway length?
Apparently you aren't the only person who wondered this; the FAA actually has it in an FAQ:
What is the significance of a runway 8069 feet in length and why are two different aerodrome symbols used to depict hard surface runways on Sectional charts?
For purposes of airport depiction, specialists represent a runway between 7970 and 8069 feet in length as 8000 feet, which equates to a line 0.192 inches in length on the Sectional chart scale. In this case, a circular aerodrome symbol is used.
If a runway is between 8070 and 8169 feet in length, specialists round to 8100 feet, which equates to a line 0.1944 inches in length on the sectional chart scale. This line is too long to fit into the largest circular aerodrome symbol FAA has available. Therefore, specialists place a line-work around the runway pattern forming a polygon (enclosed shape) for anything over 8069 feet in length.
Specialists also place these polygons around the runway pattern of aerodromes with multiple runways that are less than 8069 feet, in cases where the multiple runway pattern does not fit into the largest, circular aerodrome symbol.