Multiply. (2 * 10^1)(2 * 10^2) Choices: (A)7 * 10^2 (B)4 * 10^2 (C)7 * 10^3 (D)4 * 10^3

Identify Coefficients and Power Terms: We have: (2 × 10^1)(2 × 10^2) Group the coefficients and power terms together. Coefficients: 2 and 2 Power terms: 10^1 and 10^2Multiply Coefficients: What is 2 × 2? Multiply the coefficients. 2 × 2 = 4Combine Power Terms: Write 10^1 × 10^2 as a single power of 10. When multiplying powers with the same base, we add the exponents. 10^1 × 10^2 = 10^(1 + 2) = 10^3Write Final Answer: We found: Coefficient = 4 Power term = 10^3 Write the final answer in scientific notation. Substitute 4 for a and 3 for b in a × 10^b. Scientific notation: 4 × 10^3

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

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Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

7 \times 10^2

\newline

(B)

4 \times 10^2

\newline

(C)

7 \times 10^3

\newline

(D)

4 \times 10^3

Identify Coefficients and Power Terms: We have: $\newline$ $(2 \times 10^1)(2 \times 10^2)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $2$ and $2$ $\newline$ Power terms: $10^1$ and $10^2$
Multiply Coefficients: What is $2 \times 2$ ? Multiply the coefficients. $\newline$ $2 \times 2 = 4$
Combine Power Terms: Write $10^1 \times 10^2$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^1 \times 10^2$ $\newline$ $= 10^{(1 + 2)}$ $\newline$ $= 10^3$
Write Final Answer: We found: $\newline$ Coefficient = $4$ $\newline$ Power term = $10^3$ $\newline$ Write the final answer in scientific notation. Substitute $4$ for $a$ and $3$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $4 \times 10^3$