Question

A rope is measured as 98 cm, correct to the nearest cm. Find the percentage error of the measurement. Give the answer to 3 significant figures.

a) 2.04%
b) 1.02%
c) 2.06%
d) 1.03%

Answer 1

To find the percentage error, we calculate the absolute error by finding the difference between the measured value and the actual value. Then, we divide the absolute error by the actual value and multiply by 100%.

Step-by-step explanation:

To find the percentage error of a measurement, we need to compare the absolute error to the actual value. In this case, the rope is measured as 98 cm, correct to the nearest cm. The absolute error is calculated by finding the difference between the measured value (98 cm) and the actual value. Since the measurement is correct to the nearest cm, the actual value can range from 97.5 cm (98 cm - 0.5 cm) to 98.5 cm (98 cm + 0.5 cm). Therefore, the absolute error is 0.5 cm.

The percentage error is then calculated by dividing the absolute error by the actual value and multiplying by 100%. The actual value can be approximated as the average of the upper and lower limits, which is (97.5 cm + 98.5 cm) / 2 = 98 cm.

So, the percentage error is (0.5 cm / 98 cm) * 100% ≈ 0.5102% ≈ 0.511%.