1. GROUP 2 :
NORLIZAWATI MUHAMAD HASSAN
NORHASZUANI MOHD NASIR
NORMAZUIN MOHD NOOR

3. Objectives
1. Define and recognize:
 rational numbers and irrational numbers,
 natural numbers,
 whole numbers and
 integers.
2. List the numbers belonging to any subsets of R
3. State the relationship among sets of numbers.

5. Recall

3 3.142  
2
2.71828...  e
-4 0 4

6. Manual of this tutorial!
 This tutorial is designed to teach you about Real numbers.
The presentation starts with notes and examples followed
by practice problems.
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7. Irrational Natural
Numbers Numbers
Real
Numbers
Rational
Numbers Whole
Numbers
Integers

8. Naturals Numbers
Type of Definition Examples
Number
Natural The set of counting 1
Number numbers which is 24/4
also a subset of 3
N
real number √16
343

9. Whole Numbers
Type of
Definition Examples
Number
Whole 0
The set of natural
1
Number numbers plus a “0”
3
W W = {0,1,2,3,4,…} √16
343

10. Integers
Type of
Definition Examples
Number
The set of natural -√16
Integer
numbers, their -2
Z negatives and 0 0
Z={…,-3,-2,-1,0,1,2,3,…} 24/4
343

11. Rational Numbers
Type of
Number Definition Examples
A subset of real
Rational number that can be -1
Number written as a quotient ⅝
p/q where p, q ε Z -10.45
Q
and q ≠ 0 3.1414…
Q = {p/q |p, q ε Z, q ≠ 0} 5 - 43

12. Irrational Numbers
Type of
Definition Examples
Number
A subset of real
Irrational numbers that are not e
Number rational or numbers √2
whose decimal parts π
Q’ 3√(-12)
neither repeat nor
terminate. -7.4512…

13. Real Numbers Real
Numbers (R)
Rational Irrational
 Real numbers can be Numbers Numbers
(Q) (Q’)
divided into two basic
groups: Irrational
numbers and Rational Integers (Z)
numbers.
Whole
 Rational Numbers can Numbers
(W)
further be divided into 3
groups: integers, whole
Natural
numbers, and natural Numbers
numbers. (N)

14. Sets of numbers
Q 1/2, R
Z -1,-2..
W 0
Q’
N
1,2,3.. ∏ (pi)
√5
∴ Q ∪ Q' = R

15. Practice 1
Determine whether each statement is TRUE or FALSE.
1. Every counting number is an integer. True
2. Zero is a counting number. False
3. Negative six is greater than negative three. False
4. Some of the integers is natural numbers. True

16. Practice 2
Which of the following
A -1/2
numbers is irrational?
B 3.63
C 121
D 3
37

17. SORRY….
TRY AGAIN!!!

18. Well Done!

19. Practice 3
Which of the following
A 3
is a rational number?
B 
C 1/5
D 25/115

20. SORRY….
TRY AGAIN!!!

21. Well
Done!

22. Practice Makes Perfect
video

23. Exercises
Refer to:
numb3rscene@blogspot.com

24. Video

25. References
 Notes
 Math Is Fun
 MathWorld.Wolfram.com

26. YAY!!!
You have completed the tutorial on
Real Numbers!!
Congratulations!!