\begin{tabular}{l} MP Use Structure Marisol multiplies \( 3 \times 10^{-2} \) and \\ \( 4 \times 10^{-5} \) and gets \( 12 \times 10^{-7} \) as the product. What steps \\ should she take next to write the product using correct \\ scientific notation? Explain why these steps will not change \\ the value of the product. \\ \hline \\ \hline\end{tabular}

To write the product \( 12 \times 10^{-7} \) in correct scientific notation, Marisol should first adjust \( 12 \) to \( 1.2 \) and then increase the exponent of \( 10 \). This is done by moving the decimal point one place to the left, which means she should add 1 to the exponent: \( 12 \times 10^{-7} = 1.2 \times 10^{-6} \). This step doesn’t change the value because multiplying \( 1.2 \) by \( 10^{-6} \) is equivalent to multiplying \( 12 \) by \( 10^{-7} \) — it’s just a different way to express the same number. It’s like organizing your thoughts! By ensuring that the coefficient in scientific notation is between 1 and 10, you're making the number easier to read and interpret while keeping its value intact. This standardization helps scientists quickly compare and compute values without confusion, making the scientific community a bit more orderly and efficient!