Understanding the distinction between exact and inexact numbers is crucial for determining significant figures in measurements. Exact numbers are values obtained through counting or defined quantities, which have no uncertainty. For instance, if there are 125 students in a lecture, this number is exact because it results from a direct count. Similarly, a baker's dozen is defined as exactly 13, not 12.8 or any other variation.

In contrast, inexact numbers arise from measurements that inherently include some degree of uncertainty. For example, if a textbook is measured to be 12.53 inches long, this value is inexact because it may vary slightly depending on how the measurement is taken. Factors such as the precision of the measuring tool and the technique used can introduce small errors, making the number less definitive.

Recognizing these differences is essential when working with significant figures, as it helps in accurately reporting and interpreting data in scientific contexts. Exact numbers contribute to the precision of calculations without introducing uncertainty, while inexact numbers require careful consideration of their significant figures to reflect the reliability of the measurement.