To perform the division \(0.0580 / 0.681\):
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Calculate the division: \[ 0.0580 \div 0.681 \approx 0.0853 \]
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Now we need to consider significant figures. The number \(0.0580\) has three significant figures (the "0" after the "58" counts because it gives precision), while \(0.681\) has three significant figures as well.
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When dividing, the result should have the same number of significant figures as the measurement with the least number of significant figures.
Since both numbers have three significant figures, we should round our answer to three significant figures: \[ 0.0853 \text{ rounded to three significant figures is } 0.0853. \]
Thus, the final answer is: \[ \boxed{0.0853} \]
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