Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. Mt. Everest When Mt. Everest was first surveyed, the surveyors obtained a height of 29,000 ft to the nearest foot. State the range represented by this number. (The surveyors thought no one would believe a measurement of 29,000 ft, so they reported it as 29,002.) (Data from Dunham, W., The Mathematical Universe, John Wiley and Sons.)

Verified step by step guidance

1. Identify the concept of significant digits and accuracy in measurements.
2. Understand that a measurement of 29,000 ft to the nearest foot implies a range of possible true values.
3. Recognize that the range is determined by the smallest and largest values that would round to 29,000 ft.
4. Calculate the lower bound of the range as 28,999.5 ft, since any value below this would round down to 28,999 ft.
5. Calculate the upper bound of the range as 29,000.5 ft, since any value above this would round up to 29,001 ft.

Key Concepts

Significant Digits

Significant digits, or significant figures, are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. In the context of the Mt. Everest measurement, the reported height of 29,000 ft indicates that the measurement is precise to the nearest foot, meaning the actual height could range from 28,999.5 ft to 29,000.5 ft.

Measurement Range

The measurement range refers to the interval within which the true value of a measurement is expected to lie, based on the precision indicated by significant digits. For the height of Mt. Everest reported as 29,000 ft, the range can be calculated by considering the rounding to the nearest foot, which results in a range of 28,999.5 ft to 29,000.5 ft. This range reflects the uncertainty inherent in the measurement process.

Rounding and Reporting

Rounding is the process of adjusting a number to a specified degree of precision, often to make it easier to work with or to reflect the accuracy of the measurement. In this case, the surveyors rounded the height of Mt. Everest to 29,000 ft, but they also reported it as 29,002 ft to enhance credibility. This highlights the importance of how measurements are communicated and the potential implications for accuracy and perception.