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Multiply. Write your answer in scientific notation. $\newline$ $(1 \times 10^5)(5 \times 10^1)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

(1 \times 10^5)(5 \times 10^1)

\newline

______

Identify Numbers: Identify the numbers to be multiplied. $\newline$ We have: $1 \times 10^5$ ( $5$ \times $10$ ^ $1$ \) $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $1$ and $5$ $\newline$ Power terms: $10^5$ and $10^1$
Group Coefficients and Power: Multiply the coefficients. $\newline$ What is $1 \times 5$ ? $\newline$ $1 \times 5 = 5$
Multiply Coefficients: Multiply the power terms. $\newline$ Write $10^5 \times 10^1$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^5 \times 10^1$ $\newline$ $= 10^{5 + 1}$ $\newline$ $= 10^6$
Multiply Power Terms: Combine the results from Step $2$ and Step $3$ to write the final answer in scientific notation. $\newline$ Coefficient = $5$ $\newline$ Power term = $10^6$ $\newline$ Scientific notation: $5 \times 10^6$

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