I have attempted to research this topic due to curiosity, but I have yet to find a credible answer, the best I could find is this article, which has no listed sources, and the author has also done similar "click bait" style headlines with little to no evidence.
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$\begingroup$ The UK's Express newspaper strikes again ! Click bait is a good word for it. :-) This article on the Science News website quotes it as 100 million. As we're not sure how many stars are in the milky way, the black hole estimate is very rough ( we think there are about 100 to 400 billion stars ). $\endgroup$– StephenG - Help UkraineAug 19, 2017 at 22:32
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Yes as StephanG said there are thought to be 100 million black holes in our galaxy composed of approximately 100 billion stars. Most of these are thought to be stellar mass black holes. Not the super massive black hole assumed to be at the center of our galaxy. Some references are:http://hubblesite.org/explore_astronomy/black_holes/encyc_mod3_q7.html and https://www.sciencenews.org/article/we-share-milky-way-100-million-black-holes.
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$\begingroup$ Follow up question: do we have any idea what the mean mass of those black holes might me? $\endgroup$ Aug 20, 2017 at 0:15
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$\begingroup$ Well most of these formed as stellar mass black holes meaning they had a mass no larger than about 1.4 solar masses. I don't know how they have grown since forming though. $\endgroup$– NatsfanAug 20, 2017 at 0:25
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$\begingroup$ The average mass of stellar black holes that have been measured is about 10 solar masses. $\endgroup$– ProfRobAug 20, 2017 at 6:43
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$\begingroup$ @RobJeffries do you have a source on that? $\endgroup$ Aug 20, 2017 at 9:05
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$\begingroup$ @Cursed1701 There is a straightforward table on the relevant wikipedia page, with sources to the original literature. en.wikipedia.org/wiki/Stellar_black_hole $\endgroup$– ProfRobAug 20, 2017 at 14:15