1. The problem is to express $47 \times 10^{-11}$ F in engineering notation. 2. Engineering notation is a version of scientific notation where the exponent of 10 is a multiple of 3. 3. Start with the given number: $$47 \times 10^{-11}$$ 4. Rewrite $47$ as $4.7 \times 10^{1}$ to help adjust the exponent: $$4.7 \times 10^{1} \times 10^{-11} = 4.7 \times 10^{1 - 11} = 4.7 \times 10^{-10}$$ 5. Now, adjust the exponent to the nearest multiple of 3. The closest multiple of 3 to $-10$ is $-9$. 6. Express $4.7 \times 10^{-10}$ as: $$0.47 \times 10^{-9}$$ 7. Since $0.47$ is less than 1, move the decimal point one place to the right and decrease the exponent by 3 to keep the number equivalent: $$0.47 \times 10^{-9} = 470 \times 10^{-12}$$ 8. Now, $470$ is between 1 and 1000, and the exponent $-12$ is a multiple of 3, so this is valid engineering notation. **Final answer:** $$470 \times 10^{-12} \text{ F}$$