How are Fractional Shares Taxed?

So let's say I buy a share of stock, and over 20 years, I've been reinvesting the dividends. So each quarter, I acquire a new partial share of stock. So for 20 years at 4 per year, that's 80 new cost bases.

Let's say I sell in 20 years. Do I have to report each individual acquisition of the fractional share as a capital gain/loss?

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