Why are there 640 acres in a square mile?

Answer 1

The acre dates back to very old surveyor's units called chains, rods, and links. An acre is 10 square chains or 100 square rods, for example. Those units were the sizes of actual tools used when surveying. 640 is simply the conversion factor to take those amounts to square miles.

Today rods and chains are used about as often as cubits and hogsheads, but somehow the acre has survived - at least in the U.S., which AFAIK is the only country still using it to measure land. Everyone else uses hectares (1/100 of a square kilometer, or about 2.5 acres).