We know \(\frac{\Delta V}{V}=-\frac{P}{B}\)
Substituting values
\(\frac{-\frac{0.01}{100} \times V}{V}=\frac{-100}{B} \times 1.01 \times 10^5\) \(\left\{1 \,atm =1.01 \times 10^5 \,Pa\right.\) or \(\left.Nm ^{-2}\right\}\)
\(B=1.01 \times 10^{11} \,Nm ^{-2}\)