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Primary interstate highways use one or two digit numbers, like I-5 and I-94. Odd numbers run north and south; even numbers run east and west. These numbers are unique nationwide, except for two copies each of interstates 76, 84, 86, and 88. The canon of literature on this starts with ZZYZX's Interstate Page.
Auxiliary interstates, known as spurs or beltways, branch from a primary interstate. They have three digits, hence the nickname 3di for "3 digit interstate". Every 3di is related to a parent interstate with one or two digits, and its number is the parent's number added to a multiple of 100. This way we know I-180 is related to Interstate 80.
The first digit of a 3di carries additional meaning, as shown in the figure below:
An even starting digit (such as I-210 or I-465) means the 3di meets another interstate at both ends (or is a loop). These are usually bypasses or beltway routes.
An odd starting digit (such as I-195) means the 3di meets an interstate highway at only one end. These are usually spurs from a main interstate to a location some short distance away.
The rules for 3di numbers differ from 2di's. First, the "even is east/west and odd is north/south" rule does not apply, because a parent interstate and its 3di often go in different directions. Second, a 3di number is not unique nationwide -- only within the same state.
The Conventions are Often Flouted
The even and odd starting digit rules are often broken. For example, I-780 near San Francisco connects two interstates; and I-495 in New York only connects to the network at one end. These exceptions tend to generate a lot of discussion.
The reasons for a rule-breaking number can include historical intent, reluctance to change a number already in use, a lack of available numbers, or another interpretation of what makes an appropriate number.
Slang and unofficial terms
A 3di is a three-digit interstate. A 2di is either a one-digit or two-digit interstate; Interstates 5 and 15 are functionally identical and are both 2di's.
A parent is the 2di the 3di is based on. I-105's parent is I-5. A sibling is another 3di based on the same parent. In Maryland, I-795 never intersects its parent, but it does start at its sibling (I-695).
A family of 3di's are all those associated with a particular 2di, usually in one state: so Delaware's set of "x95's" are I-295 and I-495. New York is said to have used up all its x90's, because all nine possible 3di's (190 through 990) are already in use.
In the 1980s, California ran out of x80s in the Bay Area but needed a number for a new route between I-580 and I-880. (The highway itself was decades old, but the designation was new). I-238 was the result: the only 3di whose parent (I-38) has never existed. Many people consider I-238 an x80.