Indicate whether each of the following equations relating...

Indicate whether each of the following equations relating units would generate an exact set of conversion factors or an inexact set of conversion factors relative to significant figures.
a. 1 gallon $=16$ cups
b. 1 week $=7$ days
c. 1 pint $=0.4732$ liter
d. 1 mile $=5280$ feet

Key Concepts

Significant Figures

This concept refers to the digits in a number that carry meaning contributing to its precision. In conversions, significant figures play an important role when dealing with inexact conversion factors because they dictate the precision and accuracy of the converted result. Exact conversions are not constrained by significant figure rules since the conversion relationship is exact, whereas inexact factors require careful consideration of significant figures to maintain the accuracy of measurements.

Exact Conversion Factors

These are conversion factors that are defined by exact relationships rather than by experimental approximation. In many cases, the relationships between certain units are established by definition or agreement, meaning that no uncertainty is introduced when using these factors. For example, units like cups to gallons or days to weeks, where the numbers represent counting or precise definitions, furnish exact conversion factors.

Inexact Conversion Factors

These conversion factors arise from measurements or empirical determinations, meaning they come with an inherent level of uncertainty or approximation. When a conversion factor is not defined by a precise definition—such as many volume conversions between metric and customary units—the number used may only be accurate to a certain number of significant figures, indicating that the conversion is inexact.

Transcript

Please give Ace some feedback