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Multiply. $\newline$ $(2 \times 10^4)(1 \times 10^2)$ $\newline$ Choices: $\newline$ (A) $5 \times 10^6$ $\newline$ (B) $2 \times 10^8$ $\newline$ (C) $5 \times 10^8$ $\newline$ (D) $2 \times 10^6$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(2 \times 10^4)(1 \times 10^2)

\newline

Choices:

\newline

(A)

5 \times 10^6

\newline

(B)

2 \times 10^8

\newline

(C)

5 \times 10^8

\newline

(D)

2 \times 10^6

Group Coefficients and Power Terms: We have the expression $(2 \times 10^4)(1 \times 10^2)$ . First, we group the coefficients and power terms together. $\newline$ Coefficients: $2$ and $1$ $\newline$ Power terms: $10^4$ and $10^2$
Multiply Coefficients: Multiply the coefficients. What is $2 \times 1$ ? $\newline$ $2 \times 1 = 2$
Combine Power Terms: Combine the power terms $10^4 \times 10^2$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^4 \times 10^2$ $\newline$ $= 10^{(4 + 2)}$ $\newline$ $= 10^6$
Write in Scientific Notation: We found: $\newline$ Coefficient = $2$ $\newline$ Power term = $10^6$ $\newline$ Now, write the final answer in scientific notation by substituting $2$ for the coefficient and $6$ for the exponent in the form $a \times 10^b$ . $\newline$ Scientific notation: $2 \times 10^6$

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