Here is the explaination:
What is the A# and the Alien Registration Number? Are they the same thing?
Yes, these are two terms for the same thing. The A# is a case number that USCIS assigns to certain people, and then (usually, for exceptions see below) stays with you for the rest of your life, much like a Social Security Number. Most people get their A# when they apply for adjustment of status. It is also assigned if you apply for an employment authorization document (such as an F-1 OPT), a V visa, find yourself in deportation proceedings, and in a number of other situations.
Many USCIS forms ask for the A#. If you do not have one yet, simply write "None".
There actually are four separate types of A#. You can tell them apart by the number of digits and the first digit. The first kind is an eight-digit A#. These are manually assigned at local offices. If you have one of these numbers, simply treated it as if it was "0" plus the number. Nine-digit A#'s that start with the digit 1 are used for employment authorization cards, usually related to students. Nine-digit A#'s that start with the digit 3 are used for fingerprint tracking of V visa applicants. All other nine-digit A#'s (these actually always start with a 0) are permanent A#'s and remain permanently with you for life.
Therefore, the rule is: if you are asked for an A# and have one, always give this A#, regardless of whether it starts with a 0, 1 or 3. If you have both a 0-A# and a 1-A# or a 3-A#, then use the one that starts with a 0.