#### The Internet belongs to everyone. Let’s keep it that way.

Protect Net Neutrality

### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

# Real Numbers

No description
by

## Anshul Gupta

on 27 September 2014

Report abuse

#### Transcript of Real Numbers

Natural Numbers
1, 2, 3, 4, 5...............
All numbers which are...well... "Natural"!!!
Real Numbers
Whole Numbers
0
+
1, 2, 3, 4, 5....
Natural Numbers
0, 1, 2, 3, 4, 5......
Whole Numbers
......-5, -4, -3, -2, -1
+
Integers
Rational Numbers
Any number which can be written in the form of
p/q {p,q = integers; q = 0}

Ex. 2/3; 4; 0; 7/2; 6547/2143......
Irrational Numbers
A number whose exact value is a:

Non-Terminating & Non-Repeating Decimal
Ex. 0.001000100001.... ; √2, 3, π
Types of Irrational Numbers
1. Non-terminating, non-repeating
Ex. 0.313113111311111...; 5.252252225...; 0.554445554444
2. √m; where m is not a perfect square
Ex. √2, √3, √5,√53......
3. m; where m is not a perfect cube
Ex. 2, 3, 5, 53......
4. The Number π (pie). Its approx. value is 22/7. π has a value which is non-terminating, non-repeating.
/
Properties of Real Numbers
Multiplication Properties
1. Closure Property
Real Number 1 + Real Number 2 = Real Number 3
2. Associative Law
(a + b) + c = a + (b + c)
3. Commutative Law
a + b = b + a
a + 0 = 0 + a = a
a + (-a) = (-a) + a = 0
1. Closure Property
Real Number 1 x Real Number 2 = Real Number 3
2. Associative Law
(ab)c = a(bc)
3. Commutative Law
ab = ba
4. Existence of Multiplicative Identity
a . 1 = 1 . a = a
5. Existence of Multiplicative Inverse
a . (1/a) = (1/a) . a = 1
Multiplication Properties
Rationalisation
Rationalising Factor (RF)
If product of two irrational number is rational, then they are called the rationalising factor of each other
Ex. (a + b) and (a - b) are RF of each other.
Q. Find a rational number between 1/4 and 1/3.
Exercise
Q. Find five rational number between 3/5 and 4/5.
Exercise
Exercise
1. Add (3√2 + 7 √3) and (√2 - 5√3)
3. Simplify: (√13 - √6)(√13 + √6)
2. Divide 15√15 by 3√5
Exercise
1. Rationalise the denominator of:
a. 1 / (3 + √5)
b. 4 / (√7 + √2)
c. (√4 + √3) / (√4 - √3)
Exercise
2. If a and b are rational numbers and

(4 + 3√5) / (4 - 3√5) = a + b√5,

Find the value of a and b.
Class IX Refresher
Numbers whose square is non-negative
For a real no. a > 0 and rational numbers
p
&
q
i) a x a = a
p
q
(p + q)
ii) (a ) = a
p
q
pq
iii) a / a = a
p
q
(p - q)
iv) a x b = (ab)
p
p
p
Exercise
Full transcript