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Multiply. $\newline$ $(3 \times 10^3)(3 \times 10^3)$ $\newline$ Choices: $\newline$ (A) $9 \times 10^0$ $\newline$ (B) $9 \times 10^{12}$ $\newline$ (C) $9 \times 10^5$ $\newline$ (D) $9 \times 10^6$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(3 \times 10^3)(3 \times 10^3)

\newline

Choices:

\newline

(A)

9 \times 10^0

\newline

(B)

9 \times 10^{12}

\newline

(C)

9 \times 10^5

\newline

(D)

9 \times 10^6

Group Coefficients and Powers: We have the expression $3 \times 10^3$ ( $3$ \times $10$ ^ $3$ ). First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $3$ and $3$ $\newline$ Power terms: $10^3$ and $10^3$
Multiply Coefficients: Multiply the coefficients together. What is $3 \times 3$ ? $\newline$ $3 \times 3 = 9$
Combine Power Terms: Combine the power terms $10^3 \times 10^3$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^3 \times 10^3$ $\newline$ $= 10^{3 + 3}$ $\newline$ $= 10^6$
Final Scientific Notation: We found: $\newline$ Coefficient = $9$ $\newline$ Power term = $10^6$ $\newline$ Now, write the final answer in scientific notation by combining the coefficient and the power term. $\newline$ Scientific notation: $9 \times 10^6$

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