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Ch.1 - Matter, Measurement & Problem Solving

Chapter 1, Problem 79

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.
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.
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.
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.
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.