Environmental sciences

[shawngill]

A surveyor uses a tape, graduated in cm, to measure a rectangular plot of land. He records the length as 5.34 m and the breadth as 7.19 m. What would be the "best" value which could be given for the area of the plot? Explain your answer.

[gen2]

This homework question is about errors and accuracy.

The cm tape is obviously only allowing readings to be taken to the nearest cm so each reading is accurate to plus or minus 0.005m (0.5 cm)

When you multiply two numbers together, each with a margin of error, then you increase the margin of error in the product. As a rule of thumb - if you multiply together two numbers where the last decimal place is in error, then you can only quote the answer to one fewer decimal places.

Try it for yourself.
multiply together
5.335 x 7.185
5.34 x 7.19
5.345 x 7.195

All that of course does not take into account the accuracy of the tape measure itself. Is it metal? What is its coefficient of expansion? At what temperature was it calibrated? At what tempersature were the readings taken. Was the tape made of cloth? Does it stretch? How does its length change with changes in the relative humidity of the air? Are there any undulations in the ground that would mean you were not taking a straight line measurement. Were the two measurements taken at exactly 90 degrees to each other? How accurately were you able to confirm that?

I think the margin of error for each reading will be greater than the + or - 0.5cm that I used above.