Question

An engineer is estimating the weight of a steel beam. The actual weight of the beam is 272 pounds, and the engineer's estimate is 300 pounds. Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.

A) Absolute error = 28 pounds, Percent error = 10.3%
B) Absolute error = 28 pounds, Percent error = 11.8%
C) Absolute error = 18 pounds, Percent error = 6.6%
D) Absolute error = 18 pounds, Percent error = 9.1%

Answer 1

The correct answer to the student's question is A) Absolute error = 28 pounds, Percent error = 10.3%. This is found by subtracting the estimated weight from the actual weight to get the absolute error, and then dividing the absolute error by the actual weight and multiplying by 100 to get the percentage error.

Step-by-step explanation:

The question involves estimating the weight of a steel beam and calculating the absolute and percent error of an engineer's estimate compared with the actual weight. The absolute error is the difference between the estimated value and the actual value, which in this case is 300 pounds minus 272 pounds, resulting in an absolute error of 28 pounds. To find the percent error, we divide the absolute error by the actual weight and then multiply by 100 to convert it into a percentage.

The calculation for percent error is as follows: Percent Error = (Absolute Error / Actual Value) x 100%. For the given situation, Percent Error = (28 pounds / 272 pounds) x 100% which rounds to 10.3%. Therefore, the correct answer is A) Absolute error = 28 pounds, Percent error = 10.3%.