You should always give out your telephone number with the Area Code, even if not needed locally -
That's What The Parenthesis is for
After attending 2600's Circle of HOPE computer hackers conference in the summer of 2018, I visited an old friend in Buffalo New York, and stayed with her for a week before heading off to my 50th High School Reunion. In New York State's Niagara Frontier Region of Area code 716, I saw a large number of vehicles with their telephone numbers painted on the side, most without their Area Code.
I found this patently wrong. As a fellow who lives in tourist dominated Florida, where the Area Code changes every 30 miles or so, you have no idea WHERE those seven digits on the side of a panel truck or van can be located, so if you want to contact that company, you need the NPA to go with the 7D. In the old days of "Bell System Practices", phone numbers were designated by the Numbering Plan Area (Area Code), and the 7D (seven digits) that followed of the telephone number within that area. Phone numbers were referred to by telephone engineers as NPA Plus 7D, and we phone phreaks of those days wanted to be Just Like Them.
In the 1970's, the ITU (International Telecommunications Union) took up the topic of printing telephone numbers on business cards. The ITU is based in Europe, where people change Country Codes every 50 miles or so, let alone local area codes. It was determined that Country Codes would be designated with a + (plus sign), and that digits required "for the national service" would be in parenthesis. A typical number in England would look like: +44 (0) 343 222 1234 (the number for London Transport) where the Zero in parenthesis is only used if dialing the number within England, which means you would use the Zero to reach the long distance circuits instead of the 44 Country Code for the international cables.
The + character tells you to place the Country's Exit Code (00 for the UK, and most of Europe) before the 44 country code if calling this number from outside that country. (the exit code for the USA is 011 before the country code you're dialing).
Mobile phone networks have taken most of this drudgery out of the process, since they accept the + character as meainig "replace this character with the Exit Code if needed, and continue dialing the number. So in your Contact List in your mobile phone, just put the +1 311 555-1212 telephone number in for your correspondent, and the phone will do everythig it needs to. It will put the "+1" in front of the numbr to dial it if you are overseas yourself, and need to reach countries in the North American Dialing Plan (+1 followed by an Area Code), or not if you are within the USA, Canada, and assorted Carribean Islands that make up International Calling Zone 1.
Here in The States, if you are in a large district that still has old fashioned 7 Digit Dialing, you should write your telephone number as (311) 555-2368 (this example telephone number was the one found on telephone dials in old Bell System ads in magazines like the National Geographic, and Life). So in this example, where the area code is not required for dialing in the local area, the parenthesis tells us that (though most people don't realize it).
With the proliferation of 10 Digit Dialing being required in areas with Overlay Area Codes (and many places are getting Overlay NPAs), then in areas with 10 digit dialing, the phone number should be written without parenthesis.
☎️ 321-Liftoff (+1 321 543-8633)