Number of half-lives = how many times 138 days 'goes into' 966 days. [tex] \frac{966}{138} = 7[/tex] so 7 half-lives occur in 966 days.
Every half-life, the substance decays by exactly half of its original mass so we need to halve 31 seven times. [tex] \frac{31}{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} = \frac{31}{2^7} = 0.242g[/tex]
