REAL NUMBERS

3. Numbers which are used to count things are
known as NATURAL NUMBERS.

4. Eg. 1,2,3,4…………………………….

5. NEGETIVE NUMBERS
-1,-2,-3,-4………………………………
This type of numbers ,
which having a negative sign
are known as NEGATIVE NUMBERS

6. RATIONAL NUMBERS
NATURAL NUMBERS
NEGATIVE NUMBERS
ZERO, FRACTIONS AND
THEIR NEGATIVES collectively known as
RATIONAL NUMBERS

7. IRRATIONAL NUMBERS
The numbers which are
not rational are
IRRATIONALS

8. IRRATIONAL NUMBERS
Eg. √2, √3, √5, Π…………….

9. REAL NUMBERS
The numbers
RATIONALS and IRRATIONALS
Together known as REAL NUMBERS

10. NUMBER LINE

11. LINE WHICH CONTAINS ALL
REAL NUMBERS AS POINTS.

12. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9

13. RATIONAL NUMBERS
ON NUMBER LINE

14. . . . . . . . . . . . . . . . . . . . -4 -3 -2 -1 0 1/2 1 2 3 4 -3/2

15. IRRATIONAL NUMBERS
ON NUMBER LINE

16. -9-8-7 -6-5-4 -3 -2-1 √2 1 2 3 4 5 6 7 8 9
. . . . . . . . . . . . . . . . . . .

17. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 1 2 3 4 5 6 7 8 9
.Π
0

18. SMALL AND LARGE
LEFT AND RIGHT

19. WHEN WE GOES THROUGH RIGHT
SIDE OF A NUMBER LINE THE VALUE
OF THE POINTS ARE INCREASES.

20. WHEN WE GOES THROUGH LEFT SIDE
OF A NUMBER LINE THE VALUE OF THE
POINTS ARE DECREASES.

21. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9
2<x<4

22. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9
-3<x<2

23. DISTANCES

24. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9
2 UNITS

25. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9
2 UNITS

26. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9
6 UNITS

27. DISTANCES
In ALGEBRA

28. DISTANCE FROM ZERO TO
ANY POINT x
/x/

29. /x/ =
X , if x>0
-X , if x<0
0 , if x=]0

30. DISTANCE BETWEEN ANY
TWO POINTS X and Y
/X-Y/