Question

A surveyor is estimating the distance across a river. The actual distance is . The surveyor's estimate is . Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.

Answer 1

Question:

A surveyor is estimating the distance across a river. The actual distance is 284.5 m. The surveyor's estimate is 300 m. Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.

Answer:

(i) Absolute error = 15.5m

(ii) Percent error = 5.5%

Step-by-step explanation:

Given:

Actual measurement of the distance = 284.5 m

Estimated measurement of the distance by the surveyor = 300 m

(i) The absolute error is the magnitude of the difference between the estimated value measured by the surveyor and the actual value of the distance across the river.

i.e

Absolute error = | estimated value - actual value |

Absolute error = | 300m - 284.5m | = 15.5m

(ii) The percent error (% error) is given by the ratio of the absolute error to the actual value then multiplied by 100%. i.e

% error = $\frac{absoluteError}{actualValue}$ x 100%

% error = $\frac{15.5}{284.5}$ x 100%

% error = 0.05448 x 100%

% error = 5.448%

% error = 5.5%  [to the nearest tenth]