Method 1
using the relation
$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$
where $n=$ number of half lives
$n=\frac{t}{t_{1/2}}$
and $t=$ time $t>0=36$ days
$t_{1/2}=$ half life $=9$ days
$N=$ no of atom at time $t$
$N_0=$ original or initial no of atom and $\frac{N}{N_0}=$ fraction that remained
whilst $1-\frac{N}{N_0}=$ fraction decayed
Now
$$\begin{array}{rl}& \frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{1}{r/2}}={\left(\frac{1}{2}\right)}^{\frac{36}{9}}\\ & \frac{N}{N_0}={\left(\frac{1}{2}\right)}^4=2^{-4}\\ & \frac{N}{N_0}=\frac{1}{2^4}=\frac{1}{16}\end{array}$$raction that decayed
$=1-\frac{N}{N_0}$
$=1-\frac{1}{16}=\frac{15}{16}$
method - 2
$\left(\begin{array}{l}{N}_0\stackrel{9\text{ days }}{⟶}\frac{N_0}{2}\stackrel{9\text{ days }}{⟶}\frac{N_0}{4}\\ \stackrel{9\text{ dyss }}{⟶}\frac{N_0}{8}\stackrel{9\text{ dyys }}{⟶}\frac{N_0}{16},\end{array}\right)$raction remaining $=\frac{1}{16}$
Hence,raction decayed $=1-\frac{1}{16}=\frac{15}{16}$
Note: method 2 is preferable when time $t>0$ is not so large. If however $t>0$ is very large, then method 2 will not be conservative, so we employ method.