Answer:
After three half-lives, the fraction of the original sample that would remain is 1/8 or 0.125.
This is because each half-life reduces the amount of radioactive material by half. So, after one half-life, there will be 1/2 of the original amount remaining. After two half-lives, there will be 1/4 of the original amount remaining. After three half-lives, there will be 1/8 of the original amount remaining.
To put this in perspective, let's say we start with 100 radioactive atoms. After one half-life, we would have 50 atoms remaining. After two half-lives, there would be 25 atoms remaining. And after three half-lives, there would be 12.5 atoms remaining.
This exponential decay is the basis for radioisotope dating methods, where scientists can use the remaining fraction of a sample to determine how long ago it was formed or last exposed to sunlight or heat, amongst other things.