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There are many more stars in the universe than the years that the universe has been in existence, so wouldn't this mean that stars were/are forming at an astounding rate?

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It depends, on where and when. You should constrain a bit your question. Also the very first statement is not clear to me. –  Py-ser May 7 at 8:51
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That depends on your definition of what is an astounding rate. –  DrCopyPaste May 7 at 10:26

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By an estimated order of magnitude there are about $10^{22}$ in our observable universe (hundred billion galaxies with hundred billion stars, each, as a rough estimate), and the universe exits since (order of magnitude) $10^{10}$ years. Hence the average formation rate of stars has been about $10^{12}$ per year, meaning more than 10,000 per second, give or take a factor of 100. This calculation ignores stars which don't exist any more, but for an order-of-magnitude estimate numbers should be ok.

Although the star formation rate has been much higher in the younger universe than today. (One of the press releases about star formation in the early universe)

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