Question

for the pair of measurements, state which one is more accurate and which one is more precise. your weight is 49.51 kilograms. a scale at a health clinic that gives weight measurements to the nearest $\frac{1}{5}$ kilogram gives your weight as 50 kilograms. a digital scale at the gym that gives readings to the nearest 0.02 kilogram gives your weight as 49.36 kilograms. choose the correct answer below. a. the digital scale is both more accurate and more precise. b. the scale at the health clinic is both more accurate and more precise. c. the scale at the health clinic is more accurate and the digital scale is more precise. d. the digital scale is more accurate and the scale at the health clinic is more precise.

Explanation:

Step1: Understand accuracy and precision

Accuracy is closeness to true - value, precision is the level of detail. True weight is 49.51 kg.

Step2: Analyze accuracy

The digital scale reading of 49.36 kg has an error of \(|49.51 - 49.36|= 0.15\) kg. The health - clinic scale reading of 50 kg has an error of \(|49.51 - 50| = 0.49\) kg. Since \(0.15<0.49\), the digital scale is more accurate.

Step3: Analyze precision

The health - clinic scale gives measurements to the nearest \(\frac{1}{5}=0.2\) kg. The digital scale gives readings to the nearest 0.02 kg. Since 0.02 < 0.2, the digital scale is more precise.

Answer:

A. The digital scale is both more accurate and more precise.