Irrational Numbers: The Repeating Decimal Lab
In this interactive math worksheet, students investigate how decimals reveal whether a number is rational or irrational. Using an adjustable slider, they uncover more digits of each number’s decimal expansion, observe whether it terminates, repeats with a pattern, or continues endlessly, and record their findings. Through this hands-on discovery process, students learn that rational numbers have decimal expansions that terminate or repeat, while irrational numbers never repeat or end.
Designed for middle school math (Grade 8, CCSS 8.NS.A.1), this self-checking worksheet encourages pattern recognition, reasoning, and conceptual understanding of number types. Teachers can assign it as an in-class exploration or homework practice, with automatic feedback and scoring to reinforce mastery of rational and irrational numbers.
Learning Objective
In this activity, students will explore the decimal expansions of different types of numbers to discover patterns that distinguish rational and irrational numbers. By adjusting the number of visible decimal places, students will observe which decimals terminate, which repeat with a pattern, and which continue without repetition. Through this investigation, students will conclude that numbers with terminating or repeating decimal expansions are rational, while those with non-terminating, non-repeating decimals are irrational.
