What method would be typically used then?
Usually you would only see an IPv4 in its full dotted decimal notation, and with classless networking (technically there are no longer any subnets), with an appended /#, e.g. 111.111.177.11/20. Of course as subnet mask might be provided, with an IP, which also tells us the division between networking numbering and host numbering (as does the /), but does not really tell us whether we're doing classful or classless addressing.
Besides presenting the actual network number, subnet number and/or host number, as individual values, when done, don't recall anyone use dotted decimal for them, decimal yes, dotted decimal no.
How you teacher was representing the subnet value, in particular, I still believe confusing, as, again, I believe debatable how the subnet number was represented in dotted decimal.
To clarify further, (much along the lines of what @NetworkDave shows in his posts. Our 32 bit binary /20 is as follows:
nnnn nnnn | ssss ssss | ssss hhhh | hhhh hhhh n=network, s=subnet, h=host
Our subnet number is 12 bits, and spans the second and third octets (somewhat similar to the host number, also 12 bits which spans the third and fourth octets).
If you take the subnet's (or host's) 12 bits, as a single binary integer, you can convert it to a single decimal integer (basically you did the converse with the exercise you worked through with me).
The dotted decimal, used in IPv4 addresses, each decimal value represent an octet of 8 bits.
Given a host number of 1.11 I would convert that to: 0000 0001 | 0000 1011 blue bits exceed 12 bits for host number
Given a subnet (dotted decimal) number of 111.11 I would convert that to: 0110 1111 | 0000 1011 red bits not in the 12 bit range
But your teacher converts that to: 0110 1111 | 1011 because (?) we "know" subnet is using just the 4 high bits of the 3rd octet.
Cannot say, for sure, whether my approach or your teacher's is correct, as I don't recall anyone using dotted decimal this way. IPv4 dotted decimal, in at least the Wiki article (https://en.wikipedia.org/wiki/Dot-decimal_notation), appears to conform with my expectations that each decimal value represents a value for an octet unless your doing octet.24bits or octet.octet.16bits.
What your teacher appears to have done is octet.4bit (okay [?] because we know subnet number uses just the next 4 bits).
Personally, for students trying to grasp the basics of how an IPv4 number is constructed, and its dotted decimal notation, whether octet.4bits is right or wrong, I think "over the top".
BTW, I'm retired with 40+ years of IT experience. Actually a late comer to networking, as most of my professional career was in software development, including professional writing assembler level programs, where we often work with bits quite a lot.
