Question

a student measures the mass of an object five times and gets values: 50.1 g, 50.0 g, 50.2 g, 50.1 g, 50.0 g. the actual mass is 51.0 g. are the measurements precise, accurate, both, or neither? explain.

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 (true) value.

Step2: Analyze Precision

First, check the measured values: \( 50.1 \, \text{g}, 50.0 \, \text{g}, 50.2 \, \text{g}, 50.1 \, \text{g}, 50.0 \, \text{g} \). These values are all very close to each other (differing by at most \( 0.2 \, \text{g} \) from each other), so the measurements are precise.

Step3: Analyze Accuracy

The actual mass is \( 51.0 \, \text{g} \). The measured values are all around \( 50.0 - 50.2 \, \text{g} \), which is about \( 0.8 - 1.0 \, \text{g} \) away from the actual mass. So the measurements are not close to the actual value, meaning they are not accurate.

Answer:

The measurements are precise but not accurate. They are precise because the measured values are close to each other (e.g., \( 50.0 \, \text{g}, 50.1 \, \text{g}, 50.2 \, \text{g} \) are within a small range). They are not accurate because the measured values (around \( 50.0 - 50.2 \, \text{g} \)) are far from the actual mass (\( 51.0 \, \text{g} \)).