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Simplify. Your answer should be in proper scientific notation:

3(6×10^(5))

Simplify. Your answer should be in proper scientific notation: $\newline$ $3\left(6 \times 10^{5}\right)$

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Convert between standard and scientific notation

Full solution

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

\newline

3\left(6 \times 10^{5}\right)

Multiply Coefficients: Multiply the coefficients (the numbers in front of the powers of $10$ ). $\newline$ We have $3$ and $6$ as coefficients. Multiplying these gives us $3 \times 6 = 18$ .
Maintain Exponent: Since the power of $10$ is the same in both terms ( $10^{5}$ ), we do not need to do anything with the exponent during the multiplication. $\newline$ The expression now looks like $18 \times 10^{5}$ .
Check Coefficient Range: Check if the coefficient ( $18$ ) is in the proper form for scientific notation. $\newline$ The coefficient for scientific notation should be greater than or equal to $1$ and less than $10$ . Since $18$ is not in this range, we need to adjust it.
Convert Coefficient: Convert the coefficient to a number between $1$ and $10$ . To do this, we can express $18$ as $1.8 \times 10$ . We have effectively moved the decimal place one position to the left, which is equivalent to multiplying by $10$ .
Combine Powers: Combine the powers of $10$ . $\newline$ We now have $1.8 \times 10 \times 10^{5}$ . When we multiply powers of $10$ , we add the exponents. $\newline$ This gives us $1.8 \times 10^{1+5} = 1.8 \times 10^{6}$ .
Write Final Answer: Write the final answer in proper scientific notation. $\newline$ The final answer is $1.8 \times 10^{6}$ .

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