A chemist needs to know the mass of a sample of [tex]$MgCl _2$[/tex] to 5 significant digits. He puts the sample on a digital scale. This is what the scale shows:
0
0
4
0
7
If this measurement is precise enough for the chemist, round it to 5 significant digits. Otherwise, press the "No solution" button.
Answer (2)
Determine the number of significant digits in the measurement 0.0407.
The measurement 0.0407 has 3 significant digits.
Since 3 is less than 5, the measurement is not precise enough.
The final answer is \boxed{No solution}.
Explanation
Problem Analysis The chemist needs a mass measurement of M g C l 2 with 5 significant digits. The scale reads 0.0407. We need to check if this reading has at least 5 significant digits. If it does, we round it to 5 significant digits; otherwise, we report 'No solution'.
Significant Digits Leading zeros (zeros to the left of the first non-zero digit) are not significant. In the number 0.0407, the two zeros before 4 are not significant. The digits 4, 0, and 7 are significant. Thus, the number 0.0407 has 3 significant digits.
Precision Check Since the measurement 0.0407 has only 3 significant digits, and the chemist requires 5 significant digits, the measurement is not precise enough.
Final Answer Therefore, the answer is 'No solution'.
Examples
In chemistry, significant digits are crucial for accurate measurements. For instance, when preparing a solution, a chemist must measure the mass of a solute with the correct number of significant digits to achieve the desired concentration. If a balance provides a reading with fewer significant digits than required, the chemist must use a more precise instrument to ensure the accuracy of the experiment. This ensures that the final results and conclusions are reliable and valid.
The measurement 0.0407 has only 3 significant digits, as leading zeros are not counted. Since the chemist requires 5 significant digits for the mass of the sample, the measurement is not precise enough. Therefore, the answer is 'No solution'.
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