How long will it take to turn 27g of plutonium240 to 9 g

The half-life of Pu-240 is 6,561 years.

Half life can be modeled by the function

f (x) = P (0.5) ^x

P is our starting amount.

x is the number of half-lives required to equal f (x).

f (x) is the amount left after x half-lives.

9 = 27 (0.5) ^x

1/3 = 0.5^x

log (0.5) 1/3 = x

x = 1.585

6.561 years * 1.585 half-lives = 10,399.185 years.