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Simplify. Your answer should be in proper scientific notation: (2.5 ×10^(4))(4×10^(3))

Simplify. Your answer should be in proper scientific notation:\newline(2.5×104)(4×103) \left(2.5 \times 10^{4}\right)\left(4 \times 10^{3}\right)

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Full solution

Q. Simplify. Your answer should be in proper scientific notation:\newline(2.5×104)(4×103) \left(2.5 \times 10^{4}\right)\left(4 \times 10^{3}\right)
  1. Question Prompt: Question prompt: What is the product of (2.5×104)(2.5 \times 10^4) and (4×103)(4 \times 10^3) in proper scientific notation?\newlineTo multiply two numbers in scientific notation, we multiply their coefficients and add the exponents of 1010.\newlineCalculation: (2.5×104)×(4×103)=(2.5×4)×(104×103)(2.5 \times 10^4) \times (4 \times 10^3) = (2.5 \times 4) \times (10^4 \times 10^3)
  2. Calculation: Now we calculate the product of the coefficients and the sum of the exponents separately.\newlineCalculation for coefficients: 2.5×4=102.5 \times 4 = 10\newlineCalculation for exponents: 104×103=104+3=10710^4 \times 10^3 = 10^{4+3} = 10^7
  3. Calculation for Coefficients: Combine the results to get the product in scientific notation.\newlineCalculation: 10×10710 \times 10^7\newlineHowever, the coefficient 1010 is not between 11 and 9.999.99, which is required for proper scientific notation.
  4. Calculation for Exponents: To convert the coefficient to a number between 11 and 9.999.99, we can express 1010 as 1.0×1011.0 \times 10^1.\newlineCalculation: 10×107=(1.0×101)×107=1.0×101+7=1.0×10810 \times 10^7 = (1.0 \times 10^1) \times 10^7 = 1.0 \times 10^{1+7} = 1.0 \times 10^8\newlineNow the number is in proper scientific notation.

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