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.