class 10th real 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