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

Question

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

Bytelearn · Accepted Answer

Multiply Coefficients: Multiply the coefficients (2.5 and 4). Reasoning: In scientific notation, when multiplying two numbers, you multiply their coefficients separately from their powers of ten. Calculation: 2.5 × 4 = 10 Math error check: Add Exponents: Add the exponents (4 and 3) of the powers of ten. Reasoning: When multiplying powers of ten, you add the exponents according to the law of exponents for multiplication. Calculation: 10^4 × 10^3 = 10^(4+3) = 10^7 Math error check: Combine Results: Combine the results from Step 1 and Step 2 to form the product in scientific notation. Reasoning: The product of two numbers in scientific notation is the product of their coefficients multiplied by 10 raised to the sum of their exponents. Calculation: (2.5 × 10^4) × (4 × 10^3) = 10 × 10^7 Math error check: Ensure Proper Coefficient: Ensure the coefficient is between 1 and 10 for proper scientific notation. Reasoning: Proper scientific notation requires the coefficient to be a number between 1 and 10. Calculation: Since the coefficient is 10, which is not between 1 and 10, we need to adjust it. We can write 10 as 1.0 × 10^1. Math error check: Adjust Final Result: Adjust the final result to reflect the change in the coefficient. Reasoning: After changing the coefficient to fit the proper scientific notation, we need to combine it with the existing power of ten. Calculation: 1.0 × 10^1 × 10^7 = 1.0 × 10^(1+7) = 1.0 × 10^8 Math error check:

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

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