NCSSM Placement Practice Test 2025 – Complete Exam Prep

An irrational number is characterized by its inability to be expressed as a fraction of two integers. This distinct property extends to its decimal representation; an irrational number cannot be depicted as a terminating or repeating decimal. Instead, when it is expressed in decimal form, it produces a non-repeating, non-terminating series of digits.

For instance, the square root of 2 and the number π are both irrational. The decimal expansion of π is 3.14159..., with digits continuing indefinitely without repeating. Similarly, the expansion of the square root of 2 is approximately 1.414213..., which also continues infinitely without repeating a pattern. Thus, the defining trait of irrational numbers is the unique nature of their decimal representation, distinguishing them from rational numbers, which can either be expressed as a terminating decimal (like 0.75) or a repeating decimal (like 0.333...).

This clarity reinforces why the statement accurately capturing the nature of irrational numbers affirms that they cannot be expressed as terminating or repeating decimals.