Answer
29.9 hours.
Work Step by Step
Amount of radionuclide at the beginning $A_{0}=100$
Amount of radionuclide remaining
$A= 100.0-99.9=0.1$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{3.0\,h}=0.231/h$
$\ln(\frac{A_{0}}{A})=kt$
$\implies \ln(\frac{100}{0.1})=6.908=0.231\,h^{-1}\times t$
$\implies t=\frac{6.908}{0.231/h}=29.9\,h$
