Help!! I can't find the answer to this question no matter how much I try to work through it...

Question

 The radioactive isotope Caesium-137 has a half-life of 30 years and is used in medical applications, industrial gauges, and hydrology.  Find the amount of Caesium-137 left from a 100-mg sample after 180 years. Round your answer to the nearest tenth.

Answer 1

The simplest way to explain this is to note that after 180 years, you'll have been halved 180/30 = 6 times.

100(0.5)⁶ = your answer

Answer 2

180/30 = 6. Thus, we have 6 half-lives. This means we have 100 mg * (1/2)^6 = 100 * 1/64 = 25/16 mg = 1 9/16 mg = 1.5625 mg.

Rounded to the nearest tenth, this is 1.6 mg.