Is there a system to the numbering of beltways around cities? I notice a third digit in front of the interstate highway number and wonder if there is a way to know how those roads circle cities.

You might like to take a look at this web page. It has a brief
explanation of the numbering system.

Sad to say I can remember back when some of the freeways here
in Southern California had to change numbers to comply with
the new system.

The 11 from Pasadena to San Pedro harbor became the 110

The 7 from East Los Angeles to Long Beach became the 710.

Both are hooked into Interstate 10

Guess that just dated me !