class 9th part -2 introduction of irrational number exercise 1.2 and exercise 1.3

 

 Topic- Introduction of Rational numbers and their Decimal Expansions (see the full page)

 Click on this link  for introduction

 (This video is prepared by RUBINA HANDA)

https://www.youtube.com/watch?v=qhzDT3k0PBc&t=13s

 https://www.youtube.com/watch?v=Su7nym45lJw&t=6s

for hints and solutions of ex 1.3 click on this link

https://www.youtube.com/watch?v=zQo9Xf-U7Fo

        TOPIC- IRRATIONAL NUMBER AND HOW TO LOCATE IRRATIONAL NUMBER ON NUMBER LINE

Irrational number 

Irrational Numbers

An Irrational Number is a real number that cannot be written as a simple fraction.

Irrational means not Rational

l et's look at what makes a number rational or irrational ...

Rational Numbers

A Rational Number can be written as a Ratio of two integers (ie a simple fraction).

Example: 1.5 is rational, because it can be written as the ratio 3/2

Example: 7 is rational, because it can be written as the ratio 7/1

Example 0.333... (3 repeating) is also rational, because it can be written as the ratio 1/3

Irrational Numbers

But some numbers cannot be written as a ratio of two integers ...

...they are called Irrational Numbers.

Example: π (Pi) is a famous irrational number.

π = 3.1415926535897932384626433832795... (and more)

We cannot write down a simple fraction that equals Pi.
The popular approximation of ²²/₇ = 3.1428571428571... is close but not accurate.

Another clue is that the decimal goes on forever without repeating.

Cannot Be Written as a Fraction

It is irrational because it cannot be written as a ratio (or fraction),
not because it is crazy!

So we can tell if it is Rational or Irrational by trying to write the number as a simple fraction.

Example: 9.5 can be written as a simple fraction like this:

9.5 = 19/2

So it is a rational number (and so is not irrational)

Here are some more examples:

Number		As a Fraction		Rational or Irrational?
1.75		7/4		Rational
.001		111000		Rational
√2 (square root of 2)		?		Irrational !

Square Root of 2

Let's look at the square root of 2 more closely.

When we draw a square of size "1", what is the distance across the diagonal?

The answer is the square root of 2, which is 1.4142135623730950...(etc)
But it is not a number like 3, or five-thirds, or anything like that ...

... in fact we cannot write the square root of 2 using a ratio of two numbers

... and so we know it is an irrational number

 

Click on this link for introduction of irrational number and how to locate irrational number on the number line

 https://www.youtube.com/watch?v=ebOXPy9nQnU&t=936s

Home work - Note down the introduction in your fair note book and do exercise 1.2 and exercise 1.3

for hints and solutions of ex 1.2 click on this link 

https://www.youtube.com/watch?v=UbomktX0v9c

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