Questions: Chang is estimating the height of his office building. The actual height of his office building is 41 ft. Chang's estimate is 45 ft. Find the absolute error and the percent error of Chang's estimate. If necessary, round your answers to the nearest tenth. absolute error = ft percent error = %

Chang is estimating the height of his office building. The actual height of his office building is 41 ft. Chang's estimate is 45 ft. Find the absolute error and the percent error of Chang's estimate. If necessary, round your answers to the nearest tenth. absolute error = ft percent error = %

Transcript text: Chang is estimating the height his office building. The actual height of his office building is 41 ft . Chang's estimate is 45 ft . Find the absolute error and the percent error of Chang's estimate. If necessary, round your answers to the nearest tenth. absolute error $=$ $\square$ ft percent error $=$ $\square$ $\%$

Solution

Solution Steps

To find the absolute error, subtract the actual height from the estimated height. To find the percent error, divide the absolute error by the actual height and then multiply by 100 to convert it to a percentage. Finally, round the results to the nearest tenth if necessary.

Step 1: Calculate the Absolute Error

The absolute error is calculated by taking the absolute difference between the estimated height and the actual height: \[ \text{Absolute Error} = | \text{Estimated Height} - \text{Actual Height} | \] Given: \[ \text{Estimated Height} = 45 \, \text{ft}, \quad \text{Actual Height} = 41 \, \text{ft} \] \[ \text{Absolute Error} = | 45 - 41 | = 4 \, \text{ft} \]

Step 2: Calculate the Percent Error

The percent error is calculated by dividing the absolute error by the actual height and then multiplying by 100 to convert it to a percentage: \[ \text{Percent Error} = \left( \frac{\text{Absolute Error}}{\text{Actual Height}} \right) \times 100 \] \[ \text{Percent Error} = \left( \frac{4}{41} \right) \times 100 \approx 9.8\% \]