Two kinds of boundary
The zodiac has boundaries at thirty degree intervals, which decide the sign, and it has finer ones at every ten degrees, which decide the decan. Arguments about birthdays are almost always about the first kind, because they are the kind published as date ranges.
On this date the thirty degree boundaries are far away. The Sun left Cancer around ten days earlier and reaches Virgo three weeks later, so the sign holds in every year and at every hour. The ten degree boundary is a different matter, because the position sits close enough to it to be worth stating carefully.
Where the Sun actually stands
Taken at noon across every year from 1930 to 2035, the Sun on 1 August has fallen between roughly eight and a quarter and just under ten degrees of Leo. The top of that range is a fraction short of the decan edge, which means every year in the modern era keeps this date in the first band, though the later years of each leap cycle push it close.
A birth late in the evening sits slightly above the noon figure for its year, since the Sun advances a little under a degree a day. Even at the extreme, the position stays inside the first band, so the decan can be stated for this date without hedging.
Anyone wanting the single figure rather than the window needs only their year, and the difference between the extremes of the window is smaller than the Sun covers in two days.
The Saturn band of a Solar sign
The opening ten degrees of Leo belong to Saturn in the Chaldean scheme, which orders the planets by apparent speed and walks through them decan by decan around the whole zodiac. Leo itself is ruled by the Sun, so the first band puts the slowest classical planet inside the brightest sign.
The tradition makes something of the contrast: display that has to be earned, ambition with a long horizon, a reluctance to spend warmth cheaply. Those are readings handed down in the texts and not conclusions from anything measurable, so they are worth knowing as tradition and no more. The band assignment itself is arithmetic, and it does not depend on interpretation.
What is left over
Everything except the Sun stays open. The Moon crosses roughly half a sign in a day, so on this date it can begin in one sign and finish in another, and the date alone cannot say which applies to a given birth.
The Ascendant changes every few minutes and depends on the latitude of the birthplace, so all twelve signs are available on 1 August. The widget above resolves both: enter a year, an hour and a place and it returns the exact solar degree instead of the century wide band, along with the distance from the birth to the nearest sign boundary.
What the date genuinely delivers is a sign, a degree to within a small margin and a decan. Stated plainly, that is a short list, and it is longer than the one most pages about this birthday manage.
Questions people ask about this
What sign is 1 August?
Leo, in every year. The Sun is about nine degrees into the sign, roughly ten days after the ingress from Cancer, which puts it far beyond the reach of any date range rounding.
Which decan is a 1 August birthday?
The first decan of Leo, covering zero to ten degrees. The noon position stays under ten degrees in every year from 1930 to 2035, so the band holds for the whole date.
How close is this date to the next decan?
Close, but not over it. The highest noon value in the modern era is a fraction under ten degrees, so the second band begins the following day rather than this one.
Does the decan matter more than the sign?
It is more specific, which is a different thing. The sign covers a month of births and the band covers about ten days, so the band separates people the sign groups together.
Why does the degree vary at all between years?
Because the calendar year and the orbital year differ by nearly a quarter of a day. That gap accumulates for three years and is cancelled by the leap day, which makes the position oscillate rather than drift.
Can a birth time change the answer here?
Not for the sign or the band. It matters for the Moon, which can shift sign during the day, and for the rising sign and the houses, which need the exact minute and the birthplace.