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Multiply. $\newline$ $(4 \times 10^5)(1 \times 10^2)$ $\newline$ Choices: $\newline$ (A) $4 \times 10^6$ $\newline$ (B) $4 \times 10^7$ $\newline$ (C) $5 \times 10^6$ $\newline$ (D) $5 \times 10^7$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(4 \times 10^5)(1 \times 10^2)

\newline

Choices:

\newline

(A)

4 \times 10^6

\newline

(B)

4 \times 10^7

\newline

(C)

5 \times 10^6

\newline

(D)

5 \times 10^7

Group Coefficients and Powers: We have the expression $(4 \times 10^5)(1 \times 10^2)$ . First, we group the coefficients and power terms together. $\newline$ Coefficients: $4$ and $1$ $\newline$ Power terms: $10^5$ and $10^2$
Multiply Coefficients: Multiply the coefficients together. $\newline$ $4 \times 1 = 4$
Multiply Power Terms: Multiply the power terms together. When multiplying powers with the same base, we add the exponents. $10^5 \times 10^2 = 10^{5 + 2} = 10^7$
Combine Results: Combine the results from Step $2$ and Step $3$ to write the final answer in scientific notation. $\newline$ Coefficient = $4$ $\newline$ Power term = $10^7$ $\newline$ Scientific notation: $4 \times 10^7$

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