Challenge your students to classify decimals as rational or irrational! In this interactive worksheet, students examine non-terminating decimals—some repeating, some not—to decide which can be written as fractions. A hands-on way to strengthen understanding of decimal patterns and rationality.
In this engaging worksheet, students put their knowledge of rational and irrational numbers into practice by analyzing decimal expansions. Each number continues endlessly—but only some reveal repeating patterns! Students must determine whether each decimal repeats or never repeats and then classify it as rational or irrational.
Aligned with 8.NS.A.1, this activity deepens conceptual understanding of number systems by connecting fractions, decimals, and irrational values like √2 and π. It’s ideal for middle school math classes, review lessons, or digital practice. Teachers can assign it individually or in groups to encourage observation, reasoning, and discussion about how decimal behavior reveals whether a number is rational or irrational.
Students will analyze decimal expansions to determine whether each represents a rational or irrational number. By identifying whether a decimal terminates, repeats with a pattern, or continues without repetition, students will strengthen their understanding of the connection between decimal form and number classification (CCSS 8.NS.A.1).
The worksheet supports randomization, if enabled, every student will get a different set of numbers to solve.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
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