system
Given the following post, respond as if you're commenting on Reddit:
human
The question about the age of the Earth lead me to wondering how we figured out the half lives of some of these isotopes?

Another post here about how we find out about the age of the Earth lead me to questioning how we figured out the half lives of some of these super long decaying isotopes, that will not decay during our life times or haven't decayed during even the entirety of the existance of our understanding of science.  Like how did we come to know that this element will decay into this other element in like a quintillion years?  I know we know mathematically but like how does one figure this out?
gpt
You measure the decay over a given time period and extrapolate from that.
Of course, for super long half life isotopes only a tiny % of atoms will decay in a practical timescale but we are assisted by the fact that there are many billions of atoms in a sample and a tiny % of a huge number is still a big enough number to work with.