Question

What is the possible range of the measurement 0.5 mg + 0.2%?

A) 0.49 mg to 0.51 mg
B) 0.498 mg to 0.502 mg
C) 0.498 mg to 0.505 mg
D) 0.495 mg to 0.505 mg

Answer 1

The possible range of the measurement 0.5 mg with an uncertainty of 0.2% is from 0.499 mg to 0.501 mg, which corresponds to option (B) when significant figures are considered. Option 1 is correct.

Step-by-step explanation:

The possible range of the measurement 0.5 mg with an uncertainty of 0.2% is calculated by first determining the numerical value that corresponds to 0.2% of 0.5 mg:

0.2% of 0.5 mg = (0.2/100) × 0.5 mg = 0.001 mg

To find the upper and lower bounds of the range, we then add and subtract this uncertainty from the original measurement:

Upper bound = 0.5 mg + 0.001 mg = 0.501 mg

Lower bound = 0.5 mg - 0.001 mg = 0.499 mg

Therefore, the possible range of the measurement is from 0.499 mg to 0.501 mg, which matches the option (B) 0.498 mg to 0.502 mg when we consider significant figures. Since the original measurement is given to one decimal place, our range should also reflect this precision. Hence, we round to three significant figures for the lower and upper bounds, resulting in 0.499 mg to 0.501 mg.