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For example, January 1st, 2031 is written as 0.2031 since on January 1st, zero days have fully elapsed within that year.
January 2nd, 2031 is written 1.2031 and January 8th is written 10.2031 - the "10" portion representing 1 full week having elapsed, keeping in mind that this is base-7 notation. There are 7 full 7months in a year covering the first 343 (that's 7 * 7 * 7) days, and a final block of either 22 or 23 days, depending on whether or not the current year is a leap year. The common notations are those meant to be used for most human-targeted use cases.
However, in practice, calendar users are already familiar with thinking in terms of weeks, which lends itself directly to thinking in terms of a week-based numbering system. It is not expected that every 7date user would employ these arithmetic approaches; the point is instead that it is easier to work with exact week-based schedules in the 7date as opposed to the Gregorian calendar.
In other words, it is expected that the use of base-7 is more frightening than difficult to those new to it. Thus, a once-every-four-weeks schedule starting on 0. One advantage of the 7date calendar is that it coexists relatively well with the Gregorian calendar.
A concept similar to a leap year is necessary in any calendar system that respects both days and years, as these time units are built into the physical properties of our planet and solar system.
The 7date calendar is presented as a means of addressing several weak points of the Gregorian calendar.
It can be seen as a suggestion analogous to the metric system of centimeters, meters, and kilometers over the imperial system of inches, feet, and miles.
The primary disadvantage of the 7date calendar - as it would be for any new calendar system - is that no one knows about it.
This impedes the use case of communicating dates clearly to others.