Rational & Irrational Numbers
Rational vs. irrational numbers, and terminating vs. repeating decimals.
This page is a free outline of what the Rational & Irrational Numbers lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Converting Between Number Types See how fractions turn into terminating or repeating decimals — and back.
- Irrational Numbers A number is irrational if it can’t be written as any fraction of integers — its decimal runs forever without ever repeating. Examples: π, and the square root of any non-perfect-square like √2.
- Rational Numbers A number is rational if it can be written as a fraction a/b of two integers (b ≠ 0). That covers whole numbers, fractions, and any decimal that terminates or repeats — even 0.333… (= 1/3).
- Repeating Decimals A repeating decimal runs forever but repeats a pattern, like 0.333…. It’s still rational because it equals an exact fraction (0.333… = 1/3).
- Terminating Decimals A terminating decimal ends after a set number of places, like 0.75. It’s always rational because it equals a clean fraction (0.75 = 3/4).
Hover or tap a dotted ⓘ concept for a quick definition.
Inside the app, Rational & Irrational Numbers comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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