A boundary the date sits on
At noon across the years from 1930 to 2035, the Sun on 2 December has fallen between about nine and two fifths and ten and four fifths degrees of Sagittarius. The first decan of the sign ends at exactly ten degrees, and that band crosses it.
So the honest answer for this date is that the decan is year dependent. In years at the lower end of the range the Sun is still in the first face at noon; in years at the upper end it has already moved into the second. Neither can be claimed for the date as a whole.
Pages that state one face flatly for 2 December have taken a single year, or a single table, and generalised from it. That is a small error with a clear cause, and it is the sort of thing a calculation avoids and a printed span cannot.
What decides which side you fall on
Two things. The first is the year, through the leap cycle: the Sun arrives at any longitude about six hours later against the calendar each ordinary year, which lowers the noon degree, and a leap day pulls it back by nearly a whole day. Over four years the position walks down and jumps back up, and here that walk crosses a boundary.
The second is the hour of birth, together with the birthplace that fixes what your local hour meant in universal time. The Sun covers a little under a degree a day, so a birth twelve hours from noon shifts the position by about half a degree. In a year sitting close to the mark, morning and evening births land in different faces.
Neither factor can be guessed from the calendar date. Both are ordinary inputs to a calculation.
The two faces, and why the difference is large
The first face of Sagittarius belongs to Mercury under the Chaldean order and to Jupiter under the triplicity scheme. The second belongs to the Moon under the Chaldean order and to Aries, and so to Mars, under the triplicity scheme. That means crossing this boundary changes the traditional ruler under either scheme.
Tradition reads the first face as the sign undiluted, an appetite for the general case and for what things mean. The second is read through Mars as those same views taken up immediately as positions to defend, or through the Moon as the same restlessness tied to people and to somewhere to return to.
These are interpretations, and they are marked as interpretations. What matters here is that the reading on either side is not a shade of the other, so knowing which face applies is worth the calculation.
The sign, which is not in doubt
None of this touches the sun sign. Ten degrees is a third of the way through Sagittarius, and the nearest sign boundaries are the Scorpio ingress well over a week behind and the Capricorn ingress nearly three weeks ahead. No hour, year or time zone brings either within reach.
It is also worth saying what a birthday still cannot deliver. The Moon may be in either of two signs on this date depending on the hour, and the Ascendant, which moves about a degree every four minutes, cannot be estimated from a date at all.
The widget above computes your solar degree from your own year and birthplace and reports the distance to the nearest sign boundary. For 2 December the sign result will be dull and the degree will not be, because the degree is what settles the face.
Questions people ask about this
Which decan is 2 December?
It depends on the year and the hour. The noon Sun straddles the ten degree mark across the last century, so some years fall in the first face of Sagittarius and some in the second.
Is the sun sign in doubt too?
No. The Sun is about a third of the way through Sagittarius, which is far from either sign boundary. Only the decan is unsettled.
How do I find out which face I am in?
Enter your year, hour and birthplace in the widget above. It computes the actual solar longitude for that moment rather than reading a printed range.
Why do sites disagree about this date's decan?
Because most of them quote one year, or a rounded table, without saying so. Given a boundary that the date sits on, either answer will look right in some years.
Do the two faces differ much?
Under both rulership schemes the ruler changes at ten degrees, from Mercury to the Moon in the Chaldean order and from Jupiter to Mars under the triplicity scheme. The traditional readings differ accordingly.
Does being on a decan boundary weaken anything?
No. The Sun occupies one longitude at any instant and that longitude is inside one face. A boundary describes missing information, not a mixed condition.