Question
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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Simplify this solution 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: \(4.0 \times 10^{12}\).
