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Simplify. 5×10^(2)//3×10^(8)

Simplify.\newline5×1023×108 \frac{5 \times 10^{2}}{3 \times 10^{8}}

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Full solution

Q. Simplify.\newline5×1023×108 \frac{5 \times 10^{2}}{3 \times 10^{8}}
  1. 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 5×1025\times10^2 by 3×1083\times10^8.
  2. Calculate Coefficients Division: First, divide the coefficients (the numbers in front of the powers of 1010). This gives us 5÷35 \div 3.
  3. Subtract Exponents: Performing the division of the coefficients, we get 5÷3=1.666....5 \div 3 = 1.666....
  4. 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 2−82 - 8.
  5. Combine Results: Performing the subtraction of the exponents, we get 2−8=−62 - 8 = -6.
  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…×10−61.666\ldots \times 10^{-6}.
  7. 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…1.666\ldots to the nearest hundredth. This gives us 1.671.67.
  8. 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…1.666\ldots to the nearest hundredth. This gives us 1.671.67. Finally, we write the answer in scientific notation with the rounded coefficient: 1.67×10−61.67 \times 10^{-6}.

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