Question

for the pair of measurements, state which one is more accurate and which one is more precise. your weight is 49.57 kilograms. a scale at a health clinic that gives weight measurements to the nearest $\frac{1}{8}$ kilogram gives your weight as 50 kilograms. a digital scale at the gym that gives readings to the nearest 0.2 kilogram gives your weight as 40 kilograms. choose the correct answer below. a. the scale at the health clinic is both more accurate and more precise. b. the scale at the health clinic is more accurate and the digital scale is more precise. c. the digital scale is more accurate and the scale at the health clinic is more precise. d. the digital scale is both more accurate and more precise.

Explanation:

Step1: Define accuracy and precision

Accuracy is closeness to true value. Precision is the level of detail in measurement. True weight is 49.57 kg.

Step2: Analyze health - clinic scale

Health - clinic scale gives weight to nearest $\frac{1}{8}= 0.125$ kg and measures 50 kg. Error is $|50 - 49.57|=0.43$ kg.

Step3: Analyze digital scale

Digital scale gives weight to nearest 0.2 kg and measures 40 kg. Error is $|40 - 49.57| = 9.57$ kg.

Step4: Compare accuracy and precision

The health - clinic scale has a smaller error (more accurate) and measures to a smaller unit (more precise).

Answer:

A. The scale at the health clinic is both more accurate and more precise.