Which numbers are exact (and therefore have an unlimited number of significant figures)? a. p = 3.14 b. 12 in = 1 ft c. EPA gas mileage rating of 26 miles per gallon d. 1 gross = 144

Verified step by step guidance

1. Identify the nature of each number given in the options to determine if it is an exact number or an approximation. Exact numbers are counted or defined quantities with no uncertainty.
2. Analyze option a, p = 3.14, which is an approximation of the mathematical constant pi (π). Since pi is an irrational number, 3.14 is a rounded value and not exact.
3. Consider option b, 12 in = 1 ft. This is a defined conversion factor in the imperial measurement system where 1 foot is exactly defined as 12 inches. Therefore, it is an exact number.
4. Evaluate option c, EPA gas mileage rating of 26 miles per gallon. This is a measured value and subject to testing variability and rounding, hence it is not an exact number.
5. Review option d, 1 gross = 144. This is a defined quantity where 'gross' specifically means 144 items. As a defined count, it is an exact number.

Key Concepts

Exact Numbers

Exact numbers are values that are counted or defined quantities, which have no uncertainty and therefore an infinite number of significant figures. Examples include counts of objects (like 12 eggs) or defined relationships (like 1 foot = 12 inches). These numbers are not subject to measurement error, making them precise.

Significant Figures

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. Understanding significant figures is crucial for accurately reporting measurements and calculations in scientific contexts.

Measurement Uncertainty

Measurement uncertainty refers to the doubt that exists about the result of any measurement. It arises from limitations in measurement tools and techniques, and it affects how significant figures are determined. Recognizing which numbers are exact helps distinguish them from measured values that have inherent uncertainty.