supermassive black hole - Time according to the gravity of Sagittarius A?

Not at all a dumb question. As you have heard, it is true that time is affected by gravity. The stronger the gravitational field, the slower time passes. If you're far from any gravitating matter, time passes "normally".

But to answer your question, we must specify what is meant by "the black holes's time" (let's call the black hole $mathrm{BH}_mathrm{Sgr,A^*}$; see note below on the nomenclature), since it depends on how far from Sgr A* we are talking. The time pace at a distance $r$ from the center of a BH is given by
$$t = t_infty sqrt{1 - frac{r_mathrm{S}}{r}},$$
where $t_infty$ is the time "at infinity", i.e. far from the BH, and
$$r_mathrm{S} equiv frac{2GM}{c^2} simeq 3,mathrm{km},times left( frac{M}{M_odot}right)$$
is the so-called Schwarzschild radius (the "surface" of the BH), which is where not even light can escape. Here, $G$ is the gravitational constant, $M$ is the mass of the BH, $c$ is the speed of light, and $M_odot$ is the mass of the Sun.

The last equality shows that a BH with the mass of the Sun would have a radius of 3 km. The mass of $mathrm{BH}_mathrm{Sgr,A^*}$ is some 4.1 million Solar masses, so its radius is $r_mathrm{S} = 12.4$ million km.

Plugging in the other numbers, we can see that at a distance from $mathrm{BH}_mathrm{Sgr,A^*}$ of

1. 1 lightyear, time runs slower by a factor of 1.0000006557, i.e. unnoticeably.


2. 1 astronomical unit (the distance from Earth to the Sun), time runs 17% slower.


3. 1 million km from the surface, time runs slower by a factor of 3.7.


4. 1000 km from the surface, time runs slower by a factor of 111.


5. 1 km from the surface, time runs slower by a factor of ~3500.


6. 1 m from the surface, time runs more than a million times slower.


7. At the surface, time stops.

Note that this time dilation is what a distant observer (i.e. the guy with the $t_infty$ time) would measure for an observer at the distance $r$. The person at $r$ would just measure his/her own time as usual. For instance, according to point 5 above, if you were hovering 1 km from the surface, waving your hand every second, then I, choosing to stay at a safe distance of 1 lightyear but with a magically powerful telescope, would see you wave approximately once every hour. And when you run out of fuel and plummet into the BH, then when you cross the surface you wouldn't notice anything particular, but I would see you frozen in time. This is the concept of relativity.

Finally, let me use this chance to clarify something that people, including myself, often have gotten wrong: Sagittarius A (without an asterisk) is a radio source in the center of the Milky Way. It consists of three parts: Sagittarius A East (a supernova remnant), Sagittarius A West (dust and gas clouds), and Sagittarius A*, or Sgr A*, which is a very bright and compact radio source believed to be formed by a supermassive BH. Sgr A* isn't actually the BH itself. I think the BH doesn't really have a name, so I'll call it $mathrm{BH}_mathrm{Sgr,A^*}$. Maybe that's a bad name…