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Multiply. $\newline$ $(2 \times 10^5)(3 \times 10^4)$ $\newline$ Choices: $\newline$ (A) $6 \times 10^9$ $\newline$ (B) $4 \times 10^9$ $\newline$ (C) $4 \times 10^{10}$ $\newline$ (D) $6 \times 10^{10}$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(2 \times 10^5)(3 \times 10^4)

\newline

Choices:

\newline

(A)

6 \times 10^9

\newline

(B)

4 \times 10^9

\newline

(C)

4 \times 10^{10}

\newline

(D)

6 \times 10^{10}

Group Coefficients and Powers: We have the expression $2 \times 10^5$ ( $3$ \times $10$ ^ $4$ \). First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $2$ and $3$ $\newline$ Power terms: $10^5$ and $10^4$
Multiply Coefficients: Multiply the coefficients together. What is $2 \times 3$ ? $\newline$ $2 \times 3 = 6$
Combine Power Terms: Combine the power terms $10^5$ and $10^4$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^5 \times 10^4$ $\newline$ $= 10^{(5 + 4)}$ $\newline$ $= 10^9$
Write Final Answer: We have found: $\newline$ Coefficient = $6$ $\newline$ Power term = $10^9$ $\newline$ Now, write the final answer in scientific notation by combining the coefficient and the power term. $\newline$ Scientific notation: $6 \times 10^9$

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