First, we do not know precisely how many galaxies there are in the universe. There are several reasons why a precise count cannot exist with current technology and funding. Our way to determine the number of galaxies involves not just scanning of a specific region in the sky, but careful analysis to determine if what appears as a minuscule and faint dot of light is or is not a galaxy. That involves careful analysis of its spectrum of electromagnetic radiation, first to see if it has a typical spectrum of a single star or a galaxy, containing many stars, and second, to examine red shift to determine its distance and age. From several observations of specific patches of sky, astronomers extrapolate general figures.
In many regions of the sky, small galaxies may be too faint to be seen or our views of them may be blocked by other objects. This means that astronomers need to make approximations based on what can be observed and intricate mathematical models which create estimates based on the observable number of galaxies in selected quadrants and estimates of the total mass of the universe based on other factors such as its speed of expansion. There is also a problem of definition of what constitutes a galaxy versus a proto-galaxy, quasar, or Seyfert galaxy.
A rough current estimate is 200 billion galaxies, but that estimate is constantly being refined and revised.
https://www.nasa.gov/feature/goddard/2016/hubble-reveals-observable-universe-contains-10-times-more-galaxies-than-previously-thought/
https://www.space.com/17262-quasar-definition.html
The answer that the other educator posted has been true for the past two decades (or, at least we thought it was)--until this past week! In that way, your question is extremely timely!
Observations from NASA's Hubble Space Telescope in 1995 and various other astronomical measurements have suggested that the number of galaxies in the Universe is between 100 to 200 billion.
This number is being smashed by astronomers at the University of Nottingham, who are now claiming that there are 2 trillion galaxies in the observable Universe. Because the light from far away galaxies takes billions of years to reach us, images as old as those captured in 1995 do not represent all that can be seen now. The advent of newer, more advanced observational technology--such as the James Webb Space Telescope--will allow us to see and count more than ever before.
More information on this discovery can be found in The Atlantic article, "The Universe Just Got 10 Times More Interesting," which I have included a link to below.
https://www.theatlantic.com/science/archive/2016/10/so-many-galaxies/504185/
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