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Multiply. $\newline$ $(2 \times 10^1)(2 \times 10^2)$ $\newline$ Choices: $\newline$ (A) $3 \times 10^3$ $\newline$ (B) $4 \times 10^3$ $\newline$ (C) $8 \times 10^3$ $\newline$ (D) $7 \times 10^3$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

3 \times 10^3

\newline

(B)

4 \times 10^3

\newline

(C)

8 \times 10^3

\newline

(D)

7 \times 10^3

Group Coefficients and Powers: We have the expression $(2 \times 10^1)(2 \times 10^2)$ . First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $2$ and $2$ $\newline$ Power terms: $10^1$ and $10^2$
Multiply Coefficients: Multiply the coefficients together. What is $2 \times 2$ ? $\newline$ Calculation: $2 \times 2 = 4$
Combine Power Terms: Combine the power terms $10^1 \times 10^2$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ Calculation: $10^1 \times 10^2 = 10^{(1 + 2)} = 10^3$
Write in Scientific Notation: We have found the coefficient to be $4$ and the power term to be $10^3$ . Now, we write the final answer in scientific notation by combining these results. $\newline$ Scientific notation: $4 \times 10^3$

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