1. **State the problem:** We need to divide $4.37 \times 10^{8}$ by $7.13 \times 10^{-3}$ and express the answer in standard form to 3 significant figures. 2. **Write down the division of the numbers and powers of ten separately:** $$\frac{4.37 \times 10^{8}}{7.13 \times 10^{-3}} = \frac{4.37}{7.13} \times \frac{10^{8}}{10^{-3}}$$ 3. **Divide the coefficients:** $$\frac{4.37}{7.13} \approx 0.6129$$ 4. **Divide the powers of ten by subtracting exponents:** $$10^{8} \div 10^{-3} = 10^{8 - (-3)} = 10^{8 + 3} = 10^{11}$$ 5. **Combine the results:** $$0.6129 \times 10^{11}$$ 6. **Convert to proper standard form:** since $0.6129 = 6.129 \times 10^{-1}$, $$0.6129 \times 10^{11} = 6.129 \times 10^{-1} \times 10^{11} = 6.129 \times 10^{10}$$ 7. **Round to 3 significant figures:** $$6.13 \times 10^{10}$$ **Final answer:** $$6.13 \times 10^{10}$$