New dialing number
There will no longer a need to add 044 or any other prefix to the ten digits (the three digit area code plus the seven digit unique telephone number) that you now have. For instance, here in Ensenada the area code is 646 and the unique number is whatever seven digit telephone number given to you by your carrier (Telcel, ATT, etc). Some carriers used to require a prefix such as 044 others a different number and, yet, others no prefix. That will no longer exist. I'm not certain what effect international calls will have.