Chapter 1 of 5
Revision Notes
Real Numbers — Revision Notes
Punjab Board · Class 10 · Mathematics
Real Numbers revision notes for Punjab Board Class 10 Mathematics: 3 topics in quick points. Part of the Punjab Board Class 10 Mathematics syllabus.
44 questions25 flashcards3 formulas & key relations5 concepts
Interactive on Super Tutor
Studying Real Numbers? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.
Free trial, no card needed.
Key Topics to Revise
1
The Fundamental Theorem of Arithmetic
- Every composite number can be expressed as a product of primes, and this factorisation is UNIQUE (except for the order of factors).
- This is called the Fundamental Theorem of Arithmetic — it is the backbone of number theory.
- Any composite number x can be written as x = p1 × p2 × ... × pn, where p1 ≤ p2 ≤ ... ≤ pn are primes written in ascending order.
2
Revisiting Irrational Numbers – Proof by Contradiction
- An irrational number is a number that CANNOT be written in the form p/q, where p and q are integers and q ≠ 0.
- Examples of irrational numbers: √2, √3, √5, √15, π, 0.10110111011110...
- The method used to prove irrationality is called 'Proof by Contradiction' — assume the opposite of what you want to prove, then show this leads to a contradiction.
3
Step-by-Step Problem Solving Guide
- STEP 1 for HCF/LCM: Find prime factorisation of each number using factor tree or division.
- STEP 2 for HCF: Identify COMMON primes and pick the LOWEST exponent of each.
- STEP 3 for LCM: Identify ALL primes and pick the HIGHEST exponent of each.
Get complete notes with diagrams and examples
Full NotesKey Concepts
Every composite number can be expressedThis is a systematic wayThe HCF of two or moreThe LCM of two or moreFor any two positive integers
Frequently Asked Questions
What are the important topics in Real Numbers for Punjab Board Class 10 Mathematics?
Key topics in Real Numbers include The Fundamental Theorem of Arithmetic, Revisiting Irrational Numbers – Proof by Contradiction, Step-by-Step Problem Solving Guide. Study these first, then practise questions on each for the Punjab Board Class 10 board exam.
How should I revise Real Numbers for the Punjab Board Class 10 board exam?
Learn the core ideas first, then work through the 44 practice questions on Real Numbers. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Real Numbers
For serious students
Get the full Real Numbers chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Punjab Board Class 10 Mathematics. Free to start, no card needed.