Where the decan sits
Signs divide into three ten degree faces, and this is the opening one. It begins the moment the Sun enters Leo and lasts until ten degrees of the sign.
By the calendar the Sun passes through from around 23 July to around 2 August. The ingress date moves between years, since the tropical year overruns the calendar year by close to six hours before the leap day corrects it, so allow up to a day and a half of slippage at each end. A birthday on 22 or 23 July can fall in Cancer or in Leo depending on the year, before any decan question is even asked.
The Sun and Saturn on the same ten degrees
Under the triplicity method the fire decans run Aries, Leo, Sagittarius. Leo is the second fire sign, so its own decans start with the second in that list, which is Leo itself. That makes the Sun the ruler by the triplicity route.
The Chaldean order is a plain rotation, Mars, Sun, Venus, Mercury, Moon, Saturn, Jupiter, counted from zero degrees of Aries without regard to sign or element. The thirteenth decan in that count is Saturn.
The result is a decan where the schemes point at opposite ends of the traditional planetary range. Writers who quote only the triplicity answer describe this as the most concentrated Leo there is; writers using the Chaldean order describe something considerably more restrained. Neither is wrong, they are answering different questions, and the disagreement is usually invisible because the scheme goes unnamed.
What the tradition makes of the pairing
Leo on Leo is read as the sign without modification. Where the later decans lend it something of Sagittarius or Aries, this one adds nothing, so the qualities the tradition attaches to the sign, warmth, display, a strong sense of one's own authorship, are described as arriving undiluted.
Saturn is then read as a brake on exactly those qualities. The traditional associations are structure, delay, seriousness and consequence, and their presence at the head of Leo is taken to mean warmth that has to be earned rather than assumed, and recognition that arrives late if it arrives. Older texts treat the combination as demanding rather than easy, which is a claim about the reading and not a claim about outcomes.
It is worth keeping the weight of all this in proportion. Decans are old, genuinely part of the tradition, and traceable to Egyptian star lists, but they sit on top of a chart reading rather than under it.
There is a further wrinkle here that is easy to miss. The Sun rules Leo outright, so under the triplicity route the sign ruler and the decan ruler are the same body, while the Chaldean route introduces a second and quite unlike planet. Readings built on the first tend to describe a sign speaking in its own voice; readings built on the second describe something checked from outside. Knowing which you are reading explains most of the variation you will find.
Any placement, and why the degree matters
Nothing about this is limited to the Sun. Every planet and both angles fall in a decan, and the Ascendant in particular is read this way, since it is fixed by the birth time to within a degree or so. A Moon in the first decan of Leo draws on the same material.
Because the start of this decan coincides with the Leo ingress, late July birthdays are the ones most often placed wrongly by date tables. The check above computes your solar degree for your own date rather than assigning you to a printed range, which is the only way to settle a boundary case.
Questions people ask about this
What dates are the first decan of Leo?
Roughly 23 July to 2 August. The starting point is the Sun's entry into Leo, which moves by up to a day and a half between years, so birthdays in the last days of July should be checked directly.
Is the first decan of Leo ruled by the Sun or by Saturn?
Both answers are in use. The triplicity scheme keeps it with Leo and so with the Sun. The Chaldean rotation reaches Saturn at this point in the count. The schemes are simply built on different principles.
Does Saturn here mean a difficult life?
No, and the tradition does not phrase it that way. Saturn is read as adding structure, delay and consequence to the reading. What would change the interpretation is the rest of the chart, particularly where Saturn itself sits.
Is this the most Leo of the Leo decans?
That is the traditional claim under the triplicity scheme, on the grounds that no other fire sign is mixed in. Under the Chaldean order the picture is more qualified, which is a good illustration of why the scheme should be named.
Do decans work for the Moon and Ascendant?
Yes. They apply to any placement. The Ascendant is the most precise point in a chart, so decan work on it is at least as common as decan work on the Sun.
Where did decans come from?
From Egyptian star lists that divided the night sky into thirty six sections, each marked by a star or group of stars rising in turn. They were attached to the zodiac and given planetary rulers much later.