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Multiply. $\newline$ $(2 \times 10^2)(4 \times 10^2)$ $\newline$ Choices: $\newline$ (A) $8 \times 10^4$ $\newline$ (B) $6 \times 10^4$ $\newline$ (C) $8 \times 10^5$ $\newline$ (D) $6 \times 10^5$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

8 \times 10^4

\newline

(B)

6 \times 10^4

\newline

(C)

8 \times 10^5

\newline

(D)

6 \times 10^5

Group Coefficients and Power Terms: We have: $\newline$ $(2 \times 10^2)(4 \times 10^2)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $2$ and $4$ $\newline$ Power terms: $10^2$ and $10^2$
Multiply Coefficients: What is $2 \times 4$ ? Multiply the coefficients. $\newline$ $2 \times 4 = 8$
Combine Power Terms: Write $10^2 \times 10^2$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^2 \times 10^2$ $\newline$ $= 10^{(2 + 2)}$ $\newline$ $= 10^4$
Write Final Answer: We found: $\newline$ Coefficient = $8$ $\newline$ Power term = $10^4$ $\newline$ Write the final answer in scientific notation. Substitute $8$ for $a$ and $4$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $8 \times 10^4$

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