A magnitude 5.8 earthquake occurs. Estimate the total energy released using $E=10^{1.5M+4.8}$ joules. Round to two significant figures.

Step-by-step solution

1. Step 1: Substitute $M=5.8$ into the formula: $E=10^{1.5\times 5.8+4.8}$.
2. "Step 2: Compute the exponent: $1.5\times 5.8=8.7$, then $8.7+4.8=13.5$.
3. "Step 3: Evaluate $10^{13.5}=3.16\times 10^{13}$ J.
4. "Step 4: Round to two significant figures: $3.2\times 10^{13}$ J.

Concept tested: Earthquake energy calculation

Published 10 October 2026 · How this solution was prepared and checked