Question
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Multiply. Write your answer in scientific nota \( \left(8 \times 10^{14}\right)\left(5 \times 10^{-3}\right) \)

Ask by Rodriguez Evans. in the United States
Mar 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The answer is \(4 \times 10^{12}\).

Solution

Calculate or simplify the expression \( (8 \times 10^{14}) \times (5 \times 10^{-3}) \). Calculate the value by following steps: - step0: Calculate: \(\left(8\times 10^{14}\right)\left(5\times 10^{-3}\right)\) - step1: Evaluate: \(8\times 10^{14}\times 5\times 10^{-3}\) - step2: Multiply the numbers: \(40\times 10^{14}\times 10^{-3}\) - step3: Multiply: \(40\times 10^{11}\) - step4: Rewrite the number: \(4.0\times 10^{12}\) The result of multiplying \(8 \times 10^{14}\) by \(5 \times 10^{-3}\) is \(4 \times 10^{12}\) in scientific notation.

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The Deep Dive

First, multiply the coefficients: \(8 \times 5 = 40\). Next, for the powers of ten, add the exponents: \(10^{14} \times 10^{-3} = 10^{14 + (-3)} = 10^{11}\). Therefore, we have \(40 \times 10^{11}\). To express this in proper scientific notation, we need to represent 40 as \(4.0 \times 10^1\). Combining this gives us \(4.0 \times 10^1 \times 10^{11} = 4.0 \times 10^{12}\). So, the final answer is: \(4.0 \times 10^{12}\).

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