Which statement describes an irrational number?

An irrational number is defined as a number that cannot be expressed as a simple fraction, meaning there are no two integers ( a ) and ( b ) (where ( b ) is not zero) that satisfy the relationship ( \frac{a}{b} ). This characteristic is fundamental to irrational numbers, as they have decimal representations that neither terminate nor repeat, distinguishing them from rational numbers, which can be represented as exact fractions.

Examples of irrational numbers include ( \sqrt{2} ) and ( \pi ). When calculated, the decimal expansions of these numbers go on forever without repeating a pattern, confirming their status as irrational. In contrast, a rational number can always be represented in fractional form, leading to either a terminating decimal (like 0.75) or a repeating decimal (like 0.333... for ( \frac{1}{3} )).

In conclusion, the statement that an irrational number cannot be expressed as a fraction accurately encapsulates the defining feature of these numbers, making it the correct answer.