Simplify. 5×10^(2)//3×10^(8)

Divide Coefficients: To solve the problem, we need to divide two numbers in scientific notation. The notation // typically means integer division, but in the context of scientific notation, it's more likely to be a typo or a formatting issue, and the actual operation intended is division. So we will proceed with the division of 5×10^2 by 3×10^8.Calculate Coefficients Division: First, divide the coefficients (the numbers in front of the powers of 10). This gives us 5 ÷ 3.Subtract Exponents: Performing the division of the coefficients, we get 5 ÷ 3 = 1.666....Calculate Exponents Subtraction: Next, we subtract the exponent of the denominator from the exponent of the numerator to find the exponent of the result. This gives us 2 - 8.Combine Results: Performing the subtraction of the exponents, we get 2 - 8 = -6.Round to Nearest Hundredth: Now, we combine the result of the division of the coefficients with the result of the subtraction of the exponents to express the final answer in scientific notation. This gives us 1.666... × 10^(-6).Write Final Answer: Since the question prompt asks for the answer as an integer or a decimal rounded to the nearest hundredth, we need to round 1.666... to the nearest hundredth. This gives us 1.67.Finally, we write the answer in scientific notation with the rounded coefficient: 1.67 × 10^(-6).

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Simplify. $\newline$ $\frac{5 \times 10^{2}}{3 \times 10^{8}}$

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Q. Simplify.

\newline

\frac{5 \times 10^{2}}{3 \times 10^{8}}

Divide Coefficients: To solve the problem, we need to divide two numbers in scientific notation. The notation // typically means integer division, but in the context of scientific notation, it's more likely to be a typo or a formatting issue, and the actual operation intended is division. So we will proceed with the division of $5\times10^2$ by $3\times10^8$ .
Calculate Coefficients Division: First, divide the coefficients (the numbers in front of the powers of $10$ ). This gives us $5 \div 3$ .
Subtract Exponents: Performing the division of the coefficients, we get $5 \div 3 = 1.666....$
Calculate Exponents Subtraction: Next, we subtract the exponent of the denominator from the exponent of the numerator to find the exponent of the result. This gives us $2 - 8$ .
Combine Results: Performing the subtraction of the exponents, we get $2 - 8 = -6$ .
Round to Nearest Hundredth: Now, we combine the result of the division of the coefficients with the result of the subtraction of the exponents to express the final answer in scientific notation. This gives us $1.666\ldots \times 10^{-6}$ .
Write Final Answer: Since the question prompt asks for the answer as an integer or a decimal rounded to the nearest hundredth, we need to round $1.666\ldots$ to the nearest hundredth. This gives us $1.67$ .
Write Final Answer: Since the question prompt asks for the answer as an integer or a decimal rounded to the nearest hundredth, we need to round $1.666\ldots$ to the nearest hundredth. This gives us $1.67$ . Finally, we write the answer in scientific notation with the rounded coefficient: $1.67 \times 10^{-6}$ .