Home » Revision Notes for CBSE Class 6 to 12 » Class 10 Maths for Real Numbers of Chapter 1 Revision Notes

Class 10 Maths for Real Numbers of Chapter 1 Revision Notes

CBSE Class 10 Maths Chapter 1 – Real Numbers – Free PDF Download

Free PDF download of Class 10 Maths Chapter 1 – Real Numbers Revision Notes & Short Key-notes prepared by expert Mathematics teachers from latest edition of CBSE(NCERT) books.
You can also Download Maths NCERT Solutions Class 10 to help you to revise complete Syllabus and score more marks in your examinations.

 

CBSE Class 10 Maths Revision Notes Chapter 1 Real Numbers

  • Natural numbers: Counting numbers are called Natural numbers. These numbers are denoted by N = {1, 2, 3, ………}
  • Whole numbers: The collection of natural numbers along with 0 is the collection of Whole number and is denoted by W.
  • Integers: The collection of natural numbers, their negatives along with the number zero are called Integers. This collection is denoted by Z.
  • Rational number: The numbers, which are obtained by dividing two integers, are called Rational numbers. Division by zero is not defined.
  • Coprime: If HCF of two numbers is 1, then the two numbers area called relatively prime or coprime.

1. Euclid’s division lemma :
For given positive integers ‘a’ and ‘b’ there exist unique whole numbers ‘q’ and ‘r’ satisfying the relation .
Theorem: If  and  are non-zero integers, the least positive integer which is expressible as a linear combination of  and  is the HCF of  and , i.e., if  is the HCF of  and , then these exist integers  and , such that  and  is the smallest positive integer which is expressible in this form.
The HCF of  and  is denoted by HCF.
2. Euclid’s division algorithms :
HCF of any two positive integers a and b. With a > b is obtained as follows:
Step 1 : Apply Euclid’s division lemma to a and b to find q and r such that

b = Divisor
q = Quotient
r =  Remainder
Step II: If r  = 0, HCF (a,b)=b if , apply Euclid’s lemma to b and r.
Step III: Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.
3. The Fundamental Theorem of Arithmetic :
Every composite number can be expressed (factorized) as a product of primes and this factorization is unique, apart from the order in which the prime factors occur.

4. Let    to be a rational number, such that the prime factorization of ‘q’ is of the form 2m+5n, where m, n are non-negative integers. Then x has a decimal expansion which is terminating.
5. Let  be a rational number, such that the prime factorization of q is not of the form 2m+5n, where m, n are non-negative integers. Then x has a decimal expansion which is non-terminating repeating.
6.  is irrational, which p is a prime. A number is called irrational if it cannot be written in the form  where p and q are integers and 
8. If a and b are two positive integers, then HCF(a, b) x LCM(a, b) = a x b
i.e., (HCF x LCM) of two intergers = Product of intergers.
9. A rational number which when expressed in the lowest term has factors 2 or 5 in the denominator can be written as terminating decimal otherwise a non-terminating recurring decimal. In other words, if the rational number  is, such that the prime factorization of b is of form  where m and n are natural numbers, then  has a terminating decimal expansion.
10. We conclude that every rational number can be represented in the form of terminating or non-terminating recurring decimal.