Where the decan sits
Every sign is cut into three faces of ten degrees. This is the first of Sagittarius, beginning at the ingress from Scorpio and running to ten degrees of the sign.
The Sun is here for around ten days, from about 22 November to about 2 December. Those dates drift. A tropical year is nearly a quarter of a day longer than a calendar year, so ingress times creep later until a leap day pulls them back, and the effect is up to a day and a half of movement at each boundary. A birthday on 21 or 22 November may be Scorpio or Sagittarius depending on the year.
Jupiter and Mercury on the same ground
The triplicity scheme runs the fire signs in order, Aries, Leo, Sagittarius, and starts each sign's decans from itself. Sagittarius is third in that list, so its first decan is Sagittarius, ruled by Jupiter.
The Chaldean order pays no attention to that. It cycles Mars, Sun, Venus, Mercury, Moon, Saturn, Jupiter from zero degrees of Aries, and the twenty fifth decan comes out as Mercury.
Jupiter and Mercury are the classic pairing of the wide view against the close one, so the schemes here disagree about something substantial rather than about a shade of emphasis. This is exactly the sort of decan where a description that names no scheme should be treated with care, because the reader has no way to tell which half of the tradition they are being given.
What is read into the combination
Sagittarius on itself is described as the sign without dilution. The later decans lend it something of Aries and something of Leo; this one adds nothing, so what the tradition attaches to the sign arrives plain: a taste for the general case, for travel and for arguments about meaning rather than about facts. It is read as the most straightforwardly Jupiterian ten degrees of the zodiac.
Mercury, from the Chaldean side, is taken to supply what Jupiter usually skips. The associations are detail, language, the specific example and the habit of checking, and their presence at the head of Sagittarius is read as conviction that has to state its evidence. Older sources treat the mixture as awkward rather than smooth, on the grounds that the two planets want different things from the same statement.
Keep the weighting sensible. The decans are old, descended from Egyptian star lists that timed the night, and they belong properly to the tradition, but they are a second layer over the signs rather than a base beneath them.
The dispute also has a historical shape to it. Mercury and Jupiter are traditionally in each other's detriment, so a Chaldean ruler of Mercury on Jupiter's own opening decan is not a neutral fact within the system; it is a tension the older writers noticed and commented on. The triplicity reading has no such friction in it, and that alone accounts for much of the difference between the two portraits in circulation.
Any placement, and why the exact degree matters
This applies to more than the Sun. Every planet and angle falls in a decan, and astrologers read the Ascendant this way as a matter of course, since its degree comes straight from the birth time. A Moon in the first ten degrees of Sagittarius takes the same description.
Because this decan opens at a sign ingress, late November birthdays are where date tables go wrong most often. The check above computes your solar degree from your date, so instead of matching you to a printed span it tells you the degree and the decan directly.
Questions people ask about this
What dates are the first decan of Sagittarius?
Roughly 22 November to 2 December. The opening depends on the Sun's ingress from Scorpio, which moves by up to a day and a half between years, so birthdays right at the start should be calculated.
Who rules the first decan of Sagittarius?
Jupiter under the triplicity scheme, since the decan stays with Sagittarius itself. Mercury under the Chaldean order, which counts through a fixed planetary rotation from the start of Aries.
Why would Mercury rule a Sagittarius decan?
Because the Chaldean sequence takes no account of sign or element. It simply repeats seven planets in order through all thirty six decans, and Mercury falls at this point in the count.
Is this the most Sagittarian decan?
That is the traditional claim under the triplicity scheme, on the grounds that no other fire sign is mixed in. The Chaldean reading qualifies it considerably, which is why naming the scheme matters.
Do decans apply to the Moon and Ascendant?
Yes, to any placement. The Ascendant is a particularly natural fit, because it is fixed by your birth time and place to a fine degree of precision.
Are decans a modern invention?
No. They come from Egyptian star lists that divided the night into thirty six sections marked by rising stars. The planetary rulerships attached to them came later, in the Hellenistic period and after.