1. **State the problem:** Calculate the value of the expression $$\frac{3.56 \times 10^{-5} \times 5.87 \times 10^{12}}{4.03 \times 10^{3}}$$ and express the answer in standard form with 3 significant figures. 2. **Recall the rules for multiplying and dividing numbers in scientific notation:** - Multiply the coefficients (the numbers in front). - Add the exponents when multiplying powers of 10. - When dividing, divide the coefficients and subtract the exponents. 3. **Calculate the numerator:** $$3.56 \times 5.87 = 20.8972$$ $$10^{-5} \times 10^{12} = 10^{-5 + 12} = 10^{7}$$ So, numerator = $$20.8972 \times 10^{7}$$ 4. **Divide by the denominator:** Divide the coefficients: $$\frac{20.8972}{4.03} \approx 5.186$$ Subtract the exponents of 10: $$10^{7} \div 10^{3} = 10^{7 - 3} = 10^{4}$$ 5. **Combine the results:** $$5.186 \times 10^{4}$$ 6. **Express in standard form with 3 significant figures:** $$5.19 \times 10^{4}$$ **Final answer:** $$5.19 \times 10^{4}$$