Question

1. a student measures the mass of a sample as 9.47 g, 9.48 g and 9.45 g in 3 trials. the correct mass is 9.82 g. how is the precision of these measurements? why? how is the accuracy? why?

Explanation:

Step1: Define precision

Precision refers to the closeness of repeated measurements to each other.
The measured values are 9.47 g, 9.48 g, and 9.45 g. The differences between these values are small. For example, the difference between 9.47 g and 9.48 g is \(|9.48 - 9.47|= 0.01\) g, and between 9.47 g and 9.45 g is \(|9.47 - 9.45| = 0.02\) g. So, the precision is high as the values are close to one another.

Step2: Define accuracy

Accuracy refers to the closeness of a measurement to the true - value. The true value is 9.82 g. The measured values (9.47 g, 9.48 g, 9.45 g) are all significantly lower than the true value. The average of the measured values is \(\frac{9.47 + 9.48+9.45}{3}=\frac{28.4}{3}\approx9.47\) g. The difference between the average of the measured values and the true value is \(|9.82 - 9.47| = 0.35\) g. So, the accuracy is low.

Answer:

The precision is high because the repeated measurements (9.47 g, 9.48 g, 9.45 g) are close to each other. The accuracy is low because these measured values are significantly different from the correct mass of 9.82 g.