Does ":00" Mean "O'clock"?

I have not seen a written rule about "o'clock" equaling ":00" in a standard English text. I would love to have a reference for that rule. I know that many people were taught that. I have simply never seen it written as a rule.

There are three separate English rules for transcribing times.

I believe that, in our era of searchable documents, we should use time figures so that these can be found in a search.

SAID: We arrived at five.
TRANSCRIBE: We arrived at 5:00.

SAID: We arrived at five P.M.
TRANSCRIBE: We arrived at 5:00 P.M.

SAID: We arrived at five o"clock.
TRANSCRIBE: We arrived at 5:00 .......

If you want to be totally verbatim and the word "o'clock" is said, put the word into the transcript; if you think the ":00" already means "o'clock" and that this is redundant, then leave out the word.

Happy punctuating!