A typical date as Imperial scholars write it would look something like 0123456. Let's divide this code up to explain each part: The check number refers to the accuracy in the date as compared to time on Terra, with 0 being the most accurate and 9 being the least.
A 2 means that the event occurred while someone present for the event was in direct psychic contact with Terra or the Sol system.
A 3 means that an individual or organization present was in psychic contact with a 2 source while the event occurred.
To calculate this first you need to find which day of the year your event occurred on.
Using July 18th of 2005 as an example, you then determine the Julian date which is the 200th day of 2005. We do that by multiplying 200 by 24 then add the hour of the day the event occurred.
Most "recent" events in the Warhammer 40K universe occur in M41, or the 41st millennium.
If an event was in 2005 it would have occurred in M3 or M03, the 3rd millennium.
Circa is widely used in genealogy and historical writing when the dates of events are not accurately known.
When used in date ranges, circa is applied before each approximate date, while dates without circa immediately preceding them are generally assumed to be known with certainty.
Note that this is not generally used by Imperial citizens, but is simply for administrative use.
Each increment of the year fraction corresponds to approximately eight hours and forty-five minutes Terran standard.
If the Terra calendar year was 2005 then the Imperial Dating System Year would be 005.