What type of numbers cannot be expressed as fractions or decimals due to their infinite non-recurring decimal places?

The correct answer is that irrational numbers cannot be expressed as fractions or decimals due to their infinite non-recurring decimal places. By definition, irrational numbers are those that cannot be precisely represented as a ratio of two integers, which means they do not have a repeating or terminating decimal expansion. Classic examples include numbers like π (pi) and √2, which continue indefinitely without repeating any sequence of digits.

In contrast, rational numbers can be expressed as fractions (such as 1/2 or 3/4) and have either terminating decimal representations (like 0.25) or repeating decimal representations (like 0.333...). Real numbers encompass both rational and irrational numbers, thus including the whole set of numbers on the number line. Whole numbers are a distinct subset of real numbers that consist only of non-negative integers (0, 1, 2, 3, etc.) and cannot account for the infinitely varying decimal characteristics of irrational numbers. Hence, the uniqueness of irrational numbers lies in their inability to be captured as simple fractions or finite/recurring decimal representations.