To compute the expression \((6.02 \times 10^{23}) \cdot (-5.11 \times 10^{-27})\) and then divide by \(-8.23 \times 10^5\), you can follow these steps:
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Multiply the two numbers in the numerator:
- Multiply the coefficients: \(6.02 \times -5.11\)
- Multiply the powers of ten: \(10^{23} \times 10^{-27} = 10^{(23 - 27)} = 10^{-4}\)
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Calculate the coefficient: \[ 6.02 \times -5.11 = -30.7572 \]
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Combine the results: \[ (6.02 \times 10^{23}) \cdot (-5.11 \times 10^{-27}) = -30.7572 \times 10^{-4} = -3.07572 \times 10^{-3} \]
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Now, divide by \(-8.23 \times 10^{5}\):
- Divide the coefficients: \(-3.07572 \div -8.23\)
- Divide the powers of ten: \(10^{-3} \div 10^{5} = 10^{(-3 - 5)} = 10^{-8}\)
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Calculate the coefficient: \[ -3.07572 \div -8.23 \approx 0.374 \]
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Combine these results: \[ \frac{-3.07572 \times 10^{-3}}{-8.23 \times 10^{5}} \approx 0.374 \times 10^{-8} \]
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Express in proper scientific notation: \[ 0.374 \times 10^{-8} = 3.74 \times 10^{-9} \]
So the final result is:
\[ \approx 3.74 \times 10^{-9} \]