Question

1. a 100 - ft steel tape known to be only 99.98 ft long (under standard conditions) was used to record a measurement of 276.22 ft. what is the distance corrected for the erroneous tape?
2. it is required to lay out a rectangular commercial building 200.00 ft wide and 350.00 ft long. if the steel tape being used is 100.02 ft long (under standard conditions), what distance should be laid out?

Explanation:

Step1: Determine the tape - error ratio

The actual length of the tape is $L_{actual}=100.02$ ft and the nominal length is $L_{nominal} = 100$ ft. The ratio of the actual length to the nominal length is $r=\frac{L_{actual}}{L_{nominal}}=\frac{100.02}{100}=1.0002$.

Step2: Calculate the corrected distance

The measured distance is $d_{measured}=276.22$ ft. The corrected distance $d_{corrected}$ is found by multiplying the measured distance by the ratio $r$. So, $d_{corrected}=d_{measured}\times r = 276.22\times1.0002=276.275244$ ft.

Answer:

$276.28$ ft (rounded to two decimal places)