To compute the expression \( (6.02 \times 10^{23}) \times (9.63 \times 10^{-2}) \), follow these steps:
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Multiply the coefficients: \[ 6.02 \times 9.63 = 57.9796 \]
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Add the exponents: \[ 10^{23} \times 10^{-2} = 10^{(23 - 2)} = 10^{21} \]
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Combine the results: \[ 57.9796 \times 10^{21} \]
In scientific notation, it's conventional to have only one non-zero digit to the left of the decimal point. So, we can express \( 57.9796 \) as \( 5.79796 \times 10^{1} \).
Thus, the final result is: \[ 5.79796 \times 10^{1} \times 10^{21} = 5.79796 \times 10^{22} \]
So, the calculation yields: \[ \approx 5.80 \times 10^{22} \quad \text{(rounded to three significant figures)} \]
Thus, the final answer is \( 5.80 \times 10^{22} \).