Question

A peg of length 1.75m was measured by a student as 1.80m. Find the percentage error of the measurement to 1 decimal place.

a) 2.9%

b) 2.8%

c) 3%

d) 2.86%

Answer 1

The percentage error is calculated by dividing the absolute error by the actual value and multiplying by 100. The absolute error is 0.05 m, and the percentage error when rounded to one decimal place is 2.9%, corresponding to option (a).

Step-by-step explanation:

The percentage error of a measurement is calculated by the formula:

1. Determine the absolute error, which is the difference between the measured value and the actual value.
2. Calculate the percentage error by dividing the absolute error by the actual value and then multiplying by 100.

In this case, the actual length of the peg is 1.75 m, but it was measured as 1.80 m. The absolute error is therefore 1.80 m - 1.75 m = 0.05 m. To find the percentage error, we divide the absolute error by the actual length and then multiply by 100, which gives us:

(0.05 m / 1.75 m) × 100 = 2.8571... %

When rounded to one decimal place, the percentage error is 2.9%, which corresponds to option (a).