Which of the following expresses 393,500 in scientific notation? \( 39.35 \times 10^{4} \) \( 3.935 \times 10^{-6} \) \( 3.935 \times 10^{5} \) \( 0.3935 \times 10^{-6} \)

To express 393,500 in scientific notation, you want a number between 1 and 10 multiplied by a power of ten. The correct form for 393,500 is \( 3.935 \times 10^{5} \). You take the digits of 393,500, move the decimal point 5 places to the left (making it 3.935), and multiply by \( 10^5 \) to account for that shift. Scientific notation is not just a neat trick for handling large numbers; it’s a game-changer in scientific and engineering fields! Rather than writing out all those zeros, scientists can easily perform calculations, compare magnitudes, and communicate more effectively with colleagues. This notation helps avoid errors in calculations and makes it easier to visualize vast differences in number sizes.