This document defines and explains different types of real numbers: 1. Natural numbers (counting numbers like 1, 2, 3...) and whole numbers (natural numbers including 0) 2. Integers which include positive and negative whole numbers 3. Rational numbers which can be expressed as fractions like p/q where p and q are integers 4. Irrational numbers which cannot be expressed as fractions and include numbers like π 5. Real numbers which are the sum of all rational and irrational numbers.

1. REAL NUMBERS

3. Natural Numbers
Or
Counting numbers
1,2,3,4,5,6……
Whole Numbers
0,1,2,4,5,6,7........
Integers
…-3,-2,-
1,0,1,2,3….
Rational Numbers
3/2, ¼, 1/6,…..
Irrational number
3.141414…..,2.1010
0100001………
Real numbers

4. Natural Numbers

5. All the natural numbers including
zero [0] are called Whole
Numbers
These are denoted by letter ‘W’

8. The numbers which can be written in the form
where p & q are integers ; q ≠ 0
are called Rational numbers
They can be expressed as Terminating &
Non - Terminating Repeating Numbers
Example 1.5 = 3/2

9. The Non Terminating & Non Repeating Numbers are
called Irrational Numbers
These Numbers cannot be expressed in the form p/q
Examples ->
1. π 2. 1.01001001000……….
5454.112123123412345……..
74354354534.313323333343353363………
ETC.

10. The sum of all Rational &
Irrational numbers
is called Real Numbers
It is denoted by letter ‘R’

17. Fundamental theorem
of Arithmetic

18. Example for prime factorisation method:
Example 5 : Find the HCF of 96 and 404 by the
prime factorisation method. Hence, find their
LCM.
Solution : The prime factorisation of 96 and 404
gives: ,
Therefore, HCF is
Also, LCM (96, 404) =
Examples

19. Revisiting rational numbers
and their decimal expansions
Theorem:
Let x =p/q be a rational number, such that
the prime factorization of q is not of the
form 2n5m, where n, m are non-negative
integers. Then, x has a decimal expansion
which is non-terminating repeating
(recurring).

20. Without actually performing the long division, state
whether the following rational numbers will have a
terminating decimal expansion or a non-terminating
repeating decimal expansion:
29/343= 0.0845481049562682
77/210= 0.3666666666666667
35/50= 0.7
Example

21. THANK YOU
DONE BY
AKHILA PRABHAKARAN
X-A