What a degree is used for
Aspects are exact angular distances between two positions. An opposition is one hundred and eighty degrees apart, a trine is one hundred and twenty, a square is ninety, and each is allowed a small margin either side. Whether your Sun is in aspect to a planet depends on its longitude to within a few degrees, so a thirty degree sign band cannot answer the question at all.
House placement works the same way. Once a birth time and place are known, the houses are calculated as divisions of the sky, and whether the Sun falls just inside one house or just inside the next often turns on a couple of degrees. A chart summary that stops at the sign name has thrown away the number both calculations need.
How firmly the date fixes it
The whole span of noon positions on this date across more than a century is about one and a third degrees. That is the leap year cycle at work: three common years let the Sun slip about a quarter of a day back on any given date, and the added February day returns it, so the figure orbits a short arc rather than drifting.
Your own value moves a little more, because the hour of birth is worth a fraction of a degree and the birthplace decides the local clock. Even so, the date pins the Sun far more tightly than the sign name suggests, and the widget above turns your details into the specific figure.
The decan this degree belongs to
Sixteen degrees of Libra falls in the second of the sign's three ten degree bands. In the Chaldean order that band is assigned to Saturn, beneath Venus as ruler of the sign in full. Because the position on this date stays between roughly fifteen and seventeen degrees, the decan holds in every year of the range with no ambiguity.
Traditional readings treat the pairing as Venusian concern with proportion given a Saturnian edge, so the weighing has a standard behind it rather than a wish to agree. That is a description the tradition attaches to a band of longitude, and it is the level of detail at which two Libra birthdays start to differ from each other.
The placements a date cannot supply
The Moon moves about thirteen degrees a day, which means this date leaves it in one of two signs and occasionally three, depending on the hour. It is the fastest personal placement and the one readings lean on most heavily for temperament, so its absence from a date based answer is a large gap.
The ascendant is entirely open. All twelve signs come over the horizon in a rotation, so only the hour and the latitude of the birthplace can settle it. Since the ascendant fixes the house framework, the same Sun at sixteen degrees of Libra can be read a dozen different ways depending on a detail the calendar knows nothing about. The Sun does not move enough in a day for the date to compensate for any of that, which is the limit of what a birthday page can honestly claim.
Questions people ask about this
What degree of Libra is 9 October?
About fifteen and a third to sixteen and two thirds at noon, depending on the year. The hour of birth and the birthplace adjust it by a fraction, and the widget above applies both.
Why does the exact degree matter?
Aspects are measured as exact angles with a small allowance, and house cusps are calculated positions. Both need a longitude rather than a sign name, so the degree is the number that makes those parts of a chart possible.
Is there any chance this date is Scorpio?
None in the years from 1930 to 2035. Scorpio begins around the twenty third of the month, roughly a fortnight after this date, which is far more margin than the year or the birthplace can account for.
Which decan and which ruler?
The second decan of Libra, ten to twenty degrees, with Saturn as its Chaldean sub ruler. Venus rules the sign as a whole, so traditional readings apply the two together.
Do I need a birth time for the degree?
Not to get within a fraction of a degree, since the Sun moves about one degree per day. You do need it for the ascendant and often for the Moon, and for house placement of the Sun itself.
Does the sun sign describe personality?
The tradition attaches descriptions to the sign and to the decan, and those are interpretations laid over a measured position. The position is checkable, and what is read into it is a separate matter.