NYSTCE 222 – Childhood Mathematics (Grade 1-6) Practice Exam

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \) is not zero. When a rational number is converted into its decimal form, it will either terminate after a certain number of digits (finite) or enter a repeating cycle (repeating decimal). For example, the fraction \( \frac{1}{2} \) translates to 0.5 (a finite decimal), and \( \frac{1}{3} \) translates to 0.333... (a repeating decimal).

In contrast, an irrational number cannot be expressed as a simple fraction and has a non-terminating, non-repeating decimal expansion—examples include numbers like \( \sqrt{2} \) or \( \pi \). Whole numbers are a subset of rational numbers but are represented simply as whole integers without any decimal component. Complex numbers, which consist of a real and an imaginary part, are not represented in decimal forms as finite or repeating decimals. Therefore, rational numbers are uniquely characterized by their decimal representations as either finite or repeating.