This beats the approximations used in ancient Sumer (3.1065) and China (3). Try contacting their respective records bodies.
Gotta say, using 3 just feels like giving up due to laziness, even in 1200BC.
Also it’s interesting how the Chinese entries basically stop between 1400 and 1949, whereas European names are far more present during this era. Some Japanese ones, too. I wonder how comprehensive this page is.
Rounding pi to 3 is just the engineering way. It’s close enough to get the job done and then I don’t have to worry about decimal places. However, using pi=3 typically undershoots your calculations, so personally I like to use pi=4
An error margin of less than 5% (even better, biased in a known direction) is more than good enough for plenty of use cases.
An error margin of more than 25% on the other hand, is seldom acceptable.