Chapter 3 of the new Ganita Manjari book explores The World of Numbers. The Class 9 Maths Formula Sheet Chapter 3 The World of Numbers gathers the number sets, the rules for zero and signs, and the fraction and decimal rules on one clean page.
- Rules inside: about 14 rules, from the number sets to the decimal test for rational numbers.
- What they cover: zero and integer signs, fraction operations, absolute value, and irrationals.
- Why one page helps: the whole number system sits in front of you for quick revision.
This sheet is prepared by subject teachers, matched to the current 2026-27 NCERT, and checked line by line so a Class 9 student can trust every rule.
What Does the Class 9 Maths The World of Numbers Formula Sheet Cover?
The Class 9 Maths Formula Sheet Chapter 3 The World of Numbers covers the full sweep of the chapter. You get the five number sets and how they nest, Brahmagupta's rules for zero and signed integers, and the four fraction operations. It then lists equality and equivalence of fractions, absolute value, the distance between two numbers, a number that lies between two others, and the decimal test that tells rational and irrational apart. Nothing is added beyond the book.
Video Walkthrough
Source: Vedantu CBSE 10th on YouTube
The World of Numbers Class 9 Maths All Formulas at a Glance
The table below lists every rule for Chapter 3. Each formula cell is written in clean math so you can use it right away.
| Concept | Formula | What it means |
|---|---|---|
| Rational number | pq, q ≠ 0 | A ratio of two integers with non-zero denominator. |
| Nesting of sets | N ⊂ W ⊂ Z ⊂ Q ⊂ R | Each set sits inside the next. |
| Rules for zero | a + 0 = a; a × 0 = 0 | Zero leaves a number unchanged when added. |
| Signs on multiplication | same signs give +, opposite give - | A debt times a debt is a fortune. |
| Equality of fractions | ab = cd ad = bc | Cross-products match when the fractions are equal. |
| Add or subtract | ab ± cb = a ± cb | Use a common denominator first. |
| Multiply or divide | ab × cd = acbd | To divide, flip the second fraction and multiply. |
| Equivalent fractions | ab = akbk, k ≠ 0 | Same value in many forms. |
| Absolute value | |x| ≥ 0 | The distance of x from zero. |
| Distance between a, b | |a - b| | How far apart two numbers sit on the line. |
| Number between a, b | a + b2 | The average lands exactly in the middle. |
| Terminating decimal | denominator's primes are only 2 and 5 | Tells when a fraction ends cleanly. |
| Irrational number | non-terminating, non-repeating decimal | Cannot be written as pq, like √2 or π. |
When to Use Which Rule in The World of Numbers
Pick the right rule by reading what the question gives you. This short list keeps the choice quick.
- If you must name a number, check which set it fits, from N to R.
- If two signs multiply, use same signs give +, opposite give -.
- If you compare two fractions, cross-multiply and test ad = bc.
- If you add fractions, rewrite them over one denominator first.
- If you need a number between two others, take their average a+b2.
- If you must decide rational or irrational, look at the decimal expansion.
Quick Facts for The World of Numbers
The cards below hold the facts students mix up most. Keep the Class 9 Maths Formula Sheet Chapter 3 The World of Numbers next to them while you revise, and the ideas will settle faster.
How will Collegedunia's Formula Sheet Help You with The World of Numbers?
Collegedunia builds the Class 9 Maths Formula Sheet Chapter 3 The World of Numbers as one printable page for fast revision.
- 2026-27 Ganita Manjari match: Every rule follows the new book, not the old chapter order.
- Plain meaning added: Each rule has a short line saying what it does.
- Teacher checked: Subject experts verify each sign, fraction, and decimal rule.
- Free PDF: Download the sheet and keep it ready for your Class 9 annual exam.
More The World of Numbers Maths Class 9 Resources
Use the links below to open the other Collegedunia resources for this chapter.
NCERT Formula Sheet for Class 9 Maths: All Chapters
Use the table below to open the Formula Sheet for any other chapter of the new Class 9 Maths book.
| Chapter | Resource |
|---|---|
| Chapter 1 | Coordinates Formula Sheet |
| Chapter 2 | Linear Polynomials Formula Sheet |
| Chapter 3 | The World of Numbers Formula Sheet |
| Chapter 4 | Algebraic Identities Formula Sheet |
| Chapter 5 | Circles Formula Sheet |
| Chapter 6 | Perimeter and Area Formula Sheet |
| Chapter 7 | Introduction to Probability Formula Sheet |
| Chapter 8 | Sequences and Progressions Formula Sheet |
The World of Numbers Class 9 Maths Formula Sheet FAQs
Ques. Where can I download the The World of Numbers Class 9 Maths Formula Sheet PDF?
Ans. You can download the The World of Numbers Class 9 Maths Formula Sheet PDF directly from this page. Both the Normal and HD versions are free.
Ques. How many rules are in the Class 9 Maths Chapter 3 The World of Numbers Formula Sheet?
Ans. The sheet lists about 14 rules, covering number sets, zero, signs, fractions, absolute value, and the decimal test.
Ques. Is this chapter part of the new 2026-27 Ganita Manjari book?
Ans. Yes. The World of Numbers is Chapter 3 of the new Ganita Manjari book for the 2026-27 syllabus. In the older book, this was the Number Systems chapter.
Ques. How many pages is the The World of Numbers Formula Sheet PDF?
Ans. The Formula Sheet PDF runs about 2 pages, with a full rule table and a quick-reference section for last-day revision.
Ques. What is the main idea on this sheet?
Ans. The main idea is the real number line, R = Q ∪ I, which holds every rational and irrational number.
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