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SAT II Chemistry : Significant Figures

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Example Question #1 : Calculations

A crucible is known to weigh 43.4273 g. Five students in the class determine the weight of the crucible by repeated weighings on a simple balance. Using the following information, which student has done the most accurate determination?

Possible Answers:

$\text{Student 1:}$

$\begin{tabular}{l | c} Trial 1 & 43.6\\ Trial 2 & 43.4 \\ Trial 3 & 43.6 \\ Trial 4 & 43.5 \\ Trial 5 & 43.4 \\ \end{tabular}$

$\text{Student 2:}$

$\begin{tabular}{l | c} Trial 1 & 43.9\\ Trial 2 & 43.0 \\ Trial 3 & 43.3 \\ Trial 4 & 43.2 \\ Trial 5 & 43.4 \\ \end{tabular}$

$\text{Student 3:}$

$\begin{tabular}{l | c} Trial 1 & 43.9\\ Trial 2 & 43.0 \\ Trial 3 & 43.9 \\ Trial 4 & 43.0 \\ Trial 5 & 43.9 \\ \end{tabular}$

$\text{Student 5:}$

$\begin{tabular}{l | c} Trial 1 & 43.8\\ Trial 2 & 43.7 \\ Trial 3 & 43.0 \\ Trial 4 & 43.2 \\ Trial 5 & 43.9 \\ \end{tabular}$

$\text{Student 4:}$

$\begin{tabular}{l | c} Trial 1 & 43.9\\ Trial 2 & 43.9 \\ Trial 3 & 43.3 \\ Trial 4 & 43.0 \\ Trial 5 & 43.6 \\ \end{tabular}$

Correct answer:

$\text{Student 2:}$

$\begin{tabular}{l | c} Trial 1 & 43.9\\ Trial 2 & 43.0 \\ Trial 3 & 43.3 \\ Trial 4 & 43.2 \\ Trial 5 & 43.4 \\ \end{tabular}$

Explanation:

The student who has the accurate determination is that the student's whose average is closest to that of the "known" value of the crucible. Not be confused with precision, accuracy is how close the measured value is to the actual value, while precision is how close the measured values are to each other.

To answer this question, you need to calculate the averages of each students' weighings by summing them and dividing by five, since five measurements were taken.

$\text{Student 1:}\;\frac{43.6+43.4+43.6+43.5+43.4}{5}=43.5$

$\text{Student 2:}\;\frac{43.9+43.0+43.3+43.2+43.4}{5}=43.36\approx 43.4$

$\text{Student 3:}\;\frac{43.9+43.0+43.9+43.0+43.9}{5}=43.54\approx 43.5$

$\text{Student 4:}\;\frac{43.9+43.9+43.3+43.0+43.6}{5}=43.54\approx 43.5$

$\text{Student 5:}\;\frac{43.8+43.7+43.0+43.2+43.9}{5}=43.52\approx 43.5$

Student 2's data averages out to 43.36, which rounds to 43.4. This average has the smallest difference from that of the "known" value for the crucible, 43.4273 g. Student 2's data is the correct answer.

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SAT II Chemistry : Significant Figures

Study concepts, example questions & explanations for SAT II Chemistry

All SAT II Chemistry Resources

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Example Question #1 : Calculations

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