If you are just storing it for reference, you can store it as a string, but if you want to do a lookup, for example, to see if the IP address is in some table, you need a "canonical representation." Converting the entire thing to a (large) number is the right thing to do. IPv4 addresses can be stored as a long int (32 bits) but you need a 128 bit number to store an IPv6 address.
For example, all these strings are really the same IP address: 127.0.0.1, 127.000.000.001, ::1, 0:0:0:0:0:0:0:1