Source: Extra Practice

If the length of a rod is measured as L=(2.5±0.05) mL = (2.5 \pm 0.05) \text{ m}, what is the percentage error in the measurement?

Options

Option A

0.05%0.05\%

Option B

0.2%0.2\%

Option C is correct

2.0%2.0\%

Option D

5.0%5.0\%

Explanation

The measured value is L=2.5 mL = 2.5 \text{ m}. The absolute error is ΔL=0.05 m \Delta L = 0.05 \text{ m}. Fractional error is given by ΔLL=0.052.5\frac{\Delta L}{L} = \frac{0.05}{2.5}. 0.052.5=5250=150=0.02\frac{0.05}{2.5} = \frac{5}{250} = \frac{1}{50} = 0.02. Percentage error is the fractional error multiplied by 100%100\%: Percentage error =0.02×100%=2.0%= 0.02 \times 100\% = 2.0\% .