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Non US ZIPs regularily have strings in them (e.g. Dutch ZIP codes) so a string would be appropriate.

This is half right. String would be more appropriate than an integer type even if that weren't true. ZIP codes really don't have anything to do with the fundamental numerical operations that are defined for integer types.

plus zip codes can start with "0". Excel always screws this up

Obviously it's int, so you can do stuff like int zip_code = 01918 in C and then wonder why it doesn't even compile.

/s

When you say ZIP, do you mean USPS ZIP? USPS ZIP+4? Or non-US postal codes?

Or all of the above?