CBSE Class 10 Mathematics Real Numbers Notes Set A

Chapter 1: Real Numbers

Points to Remember

Key Concepts

5.Euclid’s Division Algorithm is stated for only positive integers but it can be extended for all integers except zero, i.e, b ≠ 0.

6.The numbers which can be represented in the form of p/q where q   0 and p and q are integers are called Rational numbers.

7.Irrational numbers are the numbers which are non-terminating and non-repeating.

8.Irrational numbers are used in

i.Finding the length of diagonal of a square whose sides are given.

ii.Finding the hypotenuse of a right triangle.

iii.Deducing the circumference of a circle whose radius is known.

9.Rational and irrational numbers together constitute Real numbers.

10.Terminating fractions are the numbers which leaves remainder 0 on normal division.

11.Recurring fractions are the numbers which never leave a remainder0 on normal division.

12.If p is a prime and p divides a2, then p divides q where a is a positive integer.

13. If p is a prime, then p is an irrational number.

14. The decimal expansion of rational number is either terminating or non-terminating recurring (repeating).

15. The decimal expansion of an irrational number is non-terminating, non-recurring.

16. If the decimal expansion of rational number terminates, then we can express the number in the form of p/q, where p and q are coprime, and the prime factorization of q is of the form 2n5m, where n and m are non negative integers.

17. A number ends with the digit zero if and only if it has either 2 or 5 as its prime factors.

18. The sum, difference, product and quotient of two irrational numbers need not always be irrational number.

19. There are more irrational numbers than rational numbers between two consecutive numbers.

20. Sum and product of a rational number and an irrational number is an irrational number.

21. Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

22. The prime factorisation of a composite number is unique, except for the order of its factors.

23. Highest Common Factor (HCF) is the product of the smallest power of each common prime factor in the numbers.

24. Lowest Common Multiple (LCM) is the product of the greatest power of each prime factor, involved in the numbers.

Key Formulae

Please refer to the link below for CBSE Class 10 Mathematics - Real Numbers Concepts