Question

1. a student performs an experiment to determine the density of a sugar solution. she obtains the following results: 1.07 g/ml, 1.81 g/ml, 1.93 g/ml, and 1.75 g/ml. if the actual value for the density of the sugar solution is 1.75 g/ml, which statement below best describes her results?

a. her results are precise, but not accurate.
b. her results are accurate, but not precise.
c. her results are both precise and accurate.
d. her results are neither precise nor accurate.

1. read the length of the metal bar with the correct number of significant figures.

Explanation:

Step1: Define precision and accuracy

Precision refers to how close the measured values are to each other. Accuracy refers to how close the measured values are to the actual value.

Step2: Analyze the data

The student's results are \(1.07\ g/mL\), \(1.81\ g/mL\), \(1.93\ g/mL\), and \(1.75\ g/mL\). The actual value is \(1.75\ g/mL\).

• Precision: The values \(1.07\), \(1.81\), \(1.93\), \(1.75\) are not very close to each other (there is a relatively large spread). But if we consider significant figures and experimental variability in a basic sense (assuming some minor experimental fluctuations), \(1.81\), \(1.93\), \(1.75\) are somewhat close (difference of \(0.1 - 0.18\) in the non - \(1.07\) values. If \(1.07\) is considered an outlier due to a measurement error in one trial and we focus on the majority (\(1.81\), \(1.93\), \(1.75\)) they are moderately close.
• Accuracy: One of the values (\(1.75\ g/mL\)) is equal to the actual value.

Since one value is accurate and the non - outlier values are somewhat close (assuming the outlier is a single - trial error), we can say her results are both precise (to a reasonable extent considering basic experiments) and accurate.

Answer:

C. Her results are both precise and accurate.