Lf gallium-68 has a half life of 68.3 minutes, how much of a 10.0mg sample is left after one half life? Two? Three?
One half-life -- 5.00 mg
Two -- 2.50 mg
Three -- 1.25 mg
One half-life is the time it takes for half of a radioactive sample to decay. But two half-lives does not mean the whole sample decays. In the second half-life you have only one-half of the original sample left, and half of that is what then decays.
So two half-lives leave you with one-quarter of the original sample, not zero; three half-lives leave one-eighth, etc.
Numbers in the answer are given to three significant digits matching the original specification.