Final answer:
The greatest possible error for the measurement 53.9 feet is B. 0.05 feet, representing the precision of the measurement up to one decimal place. Comparisons of rough guesstimates to calculated approximations along with an understanding of significant figures can greatly affect the accuracy of measurements. The example of the measuring tape illustrates how even good-quality instruments have inherent uncertainties that are expressed as percent uncertainty. The correct answer is option B.
Step-by-step explanation:
To find the greatest possible error for the measurement of 53.9 feet, we need to consider the precision of the measurement. The measurement is given to one decimal place, which indicates that the tenths place is the last significant figure. The greatest possible error is half of the smallest unit measured, so in this case, it is half of 0.1 feet, which is 0.05 feet. Therefore, the correct answer is B. 0.05 feet.
Understanding Measurement Uncertainty
When it comes to measurement uncertainty, a good exercise is to compare rough guesstimates with carefully calculated approximations. An early estimate of a measurement might be significantly off from the more carefully calculated value, as seen in the discussion where an initial guess was 3 inches but the more accurate approximation was closer to 10 feet. This shows how significant figures and precise calculations are crucial for obtaining reliable measurements.
Percent Uncertainty
In another example, a good-quality measuring tape has a possible error of 0.50 cm over a distance of 20 m, which can be used to calculate its percent uncertainty. In measurements like these, significant figures play an important role in conveying the precision and the certainty of the measurement.