Ch.1 - Matter, Measurement & Problem Solving

Problem 79b

Chapter 1, Problem 79b

Which numbers are exact (and therefore have an unlimited number of significant figures)? b. 12 in = 1 ft

Verified step by step guidance

Identify the type of numbers involved in the conversion factor.

Recognize that conversion factors between units within the same measurement system (e.g., inches to feet) are defined values.

Understand that defined values are considered exact numbers.

Conclude that exact numbers have an unlimited number of significant figures.

Therefore, the numbers in the conversion factor '12 in = 1 ft' are 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 quantities, which have no uncertainty and therefore an infinite number of significant figures. Examples include the number of students in a classroom or defined conversion factors, such as 12 inches in a foot. Because they are not measured, they do not contribute to the uncertainty in calculations.

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 accurately reporting measurements and results in scientific calculations, as they reflect the precision of the data.

Unit Conversion

Unit conversion involves changing a quantity expressed in one unit to another unit, often using conversion factors. In the example given, the relationship of 12 inches equaling 1 foot is a defined conversion factor, which is exact. This means that when performing calculations involving unit conversions, the exact nature of these factors ensures that the precision of the result is maintained.

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