The eighth and ninth degrees
A degree is a small unit and a birthday is a large one, so the two only meet through a calculation. Working from the ephemeris, this date has never put the noon Sun outside 7.9 to 9.3 degrees of Aries in the sampled century.
That places the birthday a degree or so from the end of the first decan and about eight days into the sign. Both facts are checkable and neither appears on a page written from a table of date ranges, which is what most birthday pages are.
The ten degree band is the part that adds information. A sign covers about thirty days of births and a decan about ten, so knowing the band narrows the group you share a position with to a third of what the sign alone implies, which is the only subdivision of a sign that most older sources use.
Why the range is so narrow
The Sun's circuit takes about 365.2422 days and the common year takes 365, so the noon Sun gains roughly a quarter of a degree each year. Every fourth year February adds a day and cancels almost exactly the accumulated gain.
Calendar and orbit therefore stay in step, and a birthday's solar position oscillates inside a band about a degree and a half wide rather than drifting across a century. Where you sit inside that band depends on your year, and the widget above computes it from your year, hour and birthplace, along with the distance to the nearest boundary.
The closing degrees of a Mars band
The first decan of Aries covers zero to ten degrees and is assigned to Mars in the Chaldean order, the same planet that rules the sign. This date sits in the final degree or two of that band before the Sun takes over the second.
Traditional sources treat the end of a band as no different in kind from its middle, since the boundaries are exact and there is no fading between them. What some of them do add is that a placement close to a division is worth checking twice, because a small error in the birth data can move it. That is practical advice rather than a reading, and it applies to any position near an edge.
The Chaldean sequence itself explains the assignment. It runs Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon and is applied continuously to the thirty six bands beginning at zero degrees of Aries, so Mars takes the first band and the Sun the second by position rather than by any special connection to the sign.
Everything an hour would add
Without a birth time the Moon can only be narrowed to two signs on this date, occasionally three, because it covers about thirteen degrees a day. With one, it resolves to a single degree.
The Ascendant needs a time and a place together, since the zodiac rises fully in a day and the rate at which each sign comes up depends on latitude. It is the most sensitive of the standard placements and the one furthest out of reach of a date.
That is the reason a sun sign describes so little. It survives having no birth time attached, which is exactly what makes it the least individual thing a chart contains.
Questions people ask about this
What sign is 29 March?
Aries, without exception in the sampled century. The equinox falls on 20 or 21 March across those years, putting this date eight or nine days into the sign.
How far into Aries is it?
Between about eight and nine degrees at noon. If you were born late in the evening or late in a leap cycle, the figure can reach into the ninth degree.
Which decan does that put me in?
The first decan of Aries, which runs to ten degrees and belongs to Mars in the Chaldean order. The second decan, ruled by the Sun, starts a degree or so beyond this date.
Should I check my decan carefully here?
It is worth doing, since the position sits close to the division. An accurate birth time and place settle it, and the widget above reports the gap in degrees rather than in days.
Does the leap day change my sign?
No. It shifts the solar degree by around three quarters of a degree, which is far too small to reach a sign boundary from this date.
What is the single most useful thing to add?
Your birth time. It fixes the Ascendant, the houses and the Moon, which between them carry most of what distinguishes one chart from another.