If you want to know the number of spectroscopically confirmed
galaxies then the number given by UV-D is roughly correct.
But the actual number of galaxies that have been observed is order of magnitudes larger.
The case I know is the Sloan Digital Sky Survey 3 (SDSS3):
they observed about a third of the sky using five different filters between optical and near infrared. Of all the objects detected 208,478,448
are galaxies. And of those 1.5 to 2 millions will have the spectrum measured by mid next year.
More info here
To these number you have to add the galaxies observed by surveys in different areas of the sky, deeper that SDSS (which means that they can seen fainter and/or more fare away objects).
By the way, if memory does not fail me, estimates gives about 10^10 galaxies in the observed universe
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