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Multiply. $\newline$ $(2 \times 10^4)(3 \times 10^5)$ $\newline$ Choices: $\newline$ (A) $8 \times 10^9$ $\newline$ (B) $4 \times 10^9$ $\newline$ (C) $3 \times 10^9$ $\newline$ (D) $6 \times 10^9$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

8 \times 10^9

\newline

(B)

4 \times 10^9

\newline

(C)

3 \times 10^9

\newline

(D)

6 \times 10^9

Group Coefficients and Powers: We have the expression $2 \times 10^4$ $3 \times 10^5$ . First, we group the coefficients $2$ and $3$ and the power terms $10^4$ and $10^5$ together.
Multiply Coefficients: Multiply the coefficients. We calculate $2 \times 3$ to get the new coefficient. $\newline$ $2 \times 3 = 6$
Combine Power Terms: Combine the power terms by adding the exponents, since the base is the same $10$ . We use the rule $10^m \times 10^n = 10^{(m+n)}$ . $\newline$ $10^4 \times 10^5 = 10^{(4 + 5)} = 10^9$
Write in Scientific Notation: We now have the new coefficient $6$ and the combined power term $10^9$ . We write the final answer in scientific notation by combining these two results. $\newline$ Scientific notation: $6 \times 10^9$

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