Perform the multiplication and express the answer in scientific notation. Choose the correct answer: \( \left(4.7 \times 10^{4}\right) \times\left(1.2 \times 10^{2}\right) \) \( 5.64 \times 10^{6} \) \( 5.9 \times 10^{6} \) \( 5.64 \times 10^{8} \) E \( 5.9 \times 10^{8} \)

To solve \( \left(4.7 \times 10^{4}\right) \times\left(1.2 \times 10^{2}\right) \), you first multiply the coefficients (4.7 and 1.2) and then add the exponents of the powers of ten. Calculating the coefficients: \( 4.7 \times 1.2 = 5.64 \). Now for the exponents: \( 10^{4} \times 10^{2} = 10^{4+2} = 10^{6} \). So combining these, you get: \( 5.64 \times 10^{6} \). The correct answer is: \( 5.64 \times 10^{6} \). Did you know that scientific notation is super handy when dealing with extremely large or small numbers, like the distance from Earth to the nearest star, a whopping \( 4.24 \times 10^{16} \) meters? It makes calculations, comparisons, or just plain writing way easier! In the world of science and engineering, proper use of scientific notation can help avoid common mistakes, like misplaced decimal points or confusion with significant figures. Remember, always keep your coefficients between 1 and 10 when you convert to scientific notation!