Exercise 3.5 Class 9 Maths | The World of Numbers | NCERT Ganita Manjari |2026-27

Class 9 Maths | Chapter 3 The World of Numbers | Exercise 3.5 (Full Solution) | Ganita Manjari NCERT 2026-27 Welcome to Brain Tree - Maths by Akshay Sir! In this video, we solve every question of Exercise 3.5 — Rational vs Irrational Numbers from the new NCERT Class 9 textbook Ganita Manjari (Volume 1) for the 2026-27 session. Step-by-step long division, the magic of cyclic numbers, and a clear side-by-side comparison that finally makes irrational numbers click. Plus a bonus on representing √2 and √3 on the number line! 📘 What You'll Learn ✅ The difference between terminating, repeating, and non-repeating decimals ✅ Long division of 1/13 — its repeating block and whether it shows cyclic properties ✅ What makes 1/7 = 0.142857… a true cyclic number ✅ How to spot a rational number from its decimal expansion ✅ How to identify an irrational number — definition and decimal-based test ✅ Side-by-side comparison: Rational ℚ vs Irrational 𝕀 with examples ✅ Why √2, √5, π are irrational but √81 is not ✅ Tricky cases — like 1.01001000100001… that look patterned but are actually irrational ✅ BONUS: Representing √2 and √3 on the number line using Pythagoras 📝 About the Chapter — The World of Numbers This chapter takes us on a journey from the dawn of counting (Lothal, Ishango Bone) → integers (Brahmagupta) → rationals → irrationals → real numbers. Exercise 3.5 is the bridge — where students finally understand that the number line isn't fully covered by fractions, and a whole new family of numbers lives in between. 📌 Why Brain Tree - Maths by Akshay Sir? 🪵 Live writing on a clean teaching canvas — no clutter, no distraction 🪵 Concept recap before every question — never memorise, always understand 🪵 100% NCERT 2026-27 syllabus aligned 🪵 Made for Indian students by an Indian teacher 🔔 Subscribe for Chapter 3 full playlist + all upcoming chapters! 👍 Like the video if it helped you 💬 Comment which question you'd like explained in more detail #Class9Maths #GanitaManjari #NCERT #Chapter3 #IrrationalNumbers #RationalNumbers #Exercise3point5 #CBSE2026 #BrainTree #MathsByAkshaySir #MathsForClass9 #NCERTMaths #Class9NCERT #CyclicNumbers #IndianEducation