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Multiply. $\newline$ $(3 \times 10^2)(2 \times 10^1)$ $\newline$ Choices: $\newline$ (A) $6 \times 10^9$ $\newline$ (B) $6 \times 10^3$ $\newline$ (C) $6 \times 10^8$ $\newline$ (D) $6 \times 10^6$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

6 \times 10^9

\newline

(B)

6 \times 10^3

\newline

(C)

6 \times 10^8

\newline

(D)

6 \times 10^6

Group Terms: We have the expression $3 \times 10^2$ ( $2$ \times $10$ ^ $1$ \). First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $3$ and $2$ $\newline$ Power terms: $10^2$ and $10^1$
Multiply Coefficients: Multiply the coefficients together. What is $3 \times 2$ ? $\newline$ $3 \times 2 = 6$
Combine Power Terms: Combine the power terms $10^2 \times 10^1$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^2 \times 10^1 = 10^{2 + 1} = 10^3$
Final Scientific Notation: We have found: $\newline$ Coefficient = $6$ $\newline$ Power term = $10^3$ $\newline$ Now, write the final answer in scientific notation by combining the coefficient and the power term. $\newline$ Scientific notation: $6 \times 10^3$

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