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Multiply. Write your answer in scientific notation. $\newline$ $(2 \times 10^2)(4 \times 10^5)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

(2 \times 10^2)(4 \times 10^5)

\newline

______

Group Coefficients and Powers: We have the expression $2 \times 10^2$ $4 \times 10^5$ . First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $2$ and $4$ $\newline$ Power terms: $10^2$ and $10^5$
Multiply Coefficients: Multiply the coefficients together. What is $2 \times 4$ ? $\newline$ Calculation: $2 \times 4 = 8$
Combine Power Terms: Combine the power terms $10^2 \times 10^5$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ Calculation: $10^2 \times 10^5 = 10^{2 + 5} = 10^7$
Write in Scientific Notation: We have found the coefficient to be $8$ and the power term to be $10^7$ . Now, we write the final answer in scientific notation by substituting $8$ for the coefficient $a$ and $7$ for the exponent $b$ in the form $a \times 10^b$ . $\newline$ Scientific notation: $8 \times 10^7$

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