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Simplify. Your answer should be in proper scientific notation:

(8×10^(2))(6.3 ×10^(5))

Simplify. Your answer should be in proper scientific notation: $\newline$ $\left(8 \times 10^{2}\right)\left(6.3 \times 10^{5}\right)$

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Add and subtract numbers written in scientific notation

Full solution

Q. Simplify. Your answer should be in proper scientific notation:

\newline

\left(8 \times 10^{2}\right)\left(6.3 \times 10^{5}\right)

Multiply Coefficients: Multiply the coefficients ( $8$ and $6.3$ ). $\newline$ To find the product of two numbers in scientific notation, first multiply their coefficients. $\newline$ Calculation: $8 \times 6.3 = 50.4$
Add Exponents: Add the exponents ( $2$ and $5$ ). $\newline$ When multiplying powers of $10$ , you add the exponents. $\newline$ Calculation: $10^2 \times 10^5 = 10^{2+5} = 10^7$
Combine Results: Combine the results from Step $1$ and Step $2$ to write the product in scientific notation. $\newline$ The product of the coefficients is $50.4$ , and the combined exponent of $10$ is $7$ . $\newline$ However, proper scientific notation requires the coefficient to be between $1$ and $10$ . Since $50.4$ is not in this range, we need to adjust it. $\newline$ Calculation: $50.4 \times 10^7$ can be rewritten as $(5.04 \times 10) \times 10^7$
Adjust Coefficient: Adjust the coefficient to proper scientific notation by factoring out a power of $10$ . $\newline$ We can rewrite $5.04 \times 10$ as $5.04 \times 10^1$ . $\newline$ Calculation: $5.04 \times 10^1 \times 10^7 = 5.04 \times 10^{1+7} = 5.04 \times 10^8$

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