Number of natural life times $\left(T_{av}\right)$ required for a first-order reaction to achieve 99.9% level of completion is :

Number of natural life times needed for the first-order reaction to achieve 99.9% level of completion is, 

$t_{99.9}=10\times t_{1/2}$

$=10\times 0.693\times t_{av}$

$=6.9\times t_{av}$

This is 6.9 times the natural life time.