Which of the following statements uses exact numbers? (a) 1 ft = 12 in. (b) 1 cal = 4.184 J (c) The height of Mt. Everest is 29,035 ft. (d) The world record for the 1-mile run, set by Morocco's Hicham el Guerrouj in July 1999, is 3 minutes, 43.13 seconds

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Identify what exact numbers are: Exact numbers are those that are counted or defined, not measured, and have an infinite number of significant figures.

Examine statement (a): '1 ft = 12 in.' This is a defined relationship between feet and inches, making it an exact number.

Examine statement (b): '1 cal = 4.184 J' This is a conversion factor between calories and joules, which is measured and not exact.

Examine statement (c): 'The height of Mt. Everest is 29,035 ft.' This is a measured value, so it is not exact.

Examine statement (d): 'The world record for the 1-mile run, set by Morocco's Hicham el Guerrouj in July 1999, is 3 minutes, 43.13 seconds.' This is a measured time, so it is not exact.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exact Numbers

Exact numbers are values that are counted or defined and have no uncertainty associated with them. They are typically whole numbers, such as the number of students in a classroom or defined relationships like 1 foot = 12 inches. These numbers are considered to have an infinite number of significant figures, making them precise and reliable for calculations.

Measured Numbers

Measured numbers are values obtained through measurement and inherently include some degree of uncertainty. For example, the height of Mt. Everest, which is measured and reported as 29,035 ft, may vary slightly depending on the method of measurement and the conditions at the time. These numbers are significant and can affect calculations due to their associated uncertainty.

Significant Figures

Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for determining the accuracy of measured numbers and for performing calculations that reflect the precision of the data involved.