Answer
$\approx 2.24\%$
Work Step by Step
The energy for R=9.0 is found as in part (a),
$9.0=\displaystyle \frac{2}{3}(\log E-11.8)$
$\displaystyle \frac{3(9.0)}{2}=\log E-11.8$
$\displaystyle \log E=\frac{3(9.0)}{2}+11.8$
$\log E= 25.6$
$E=10^{25.6}\approx 1.996\times 10^{25}$ ergs
The ratio of the energies in the 1906 and 2011 quakes:
$\displaystyle \frac{4.467\times 10^{23}}{1.996\times 10^{25}}\approx 0.02238\approx 2.24\%$
