Question

find irrational number between 2.9(bar over 9) and 3

please be fast
no explanation need​

Answer 1

Step-by-step explanation:

Given :-

2.9(bar on 9) and 3

To find :-

Find an irrational number between them?

Solution:-

Method-1:-

Given numbers are 2.9(bar on 9) and 3

2.9(bar on 9) can be written as 2.99999...

So the irrational number between them

= 2.998877654321...

Method-2:-

Given numbers are 2.9(bar on 9) and 3

Let x = 2.9(bar on 9)

=> x = 2.9999... -------(1)

Since the periodicity is 1 then we multiply (1) with 10

=> 10×x = 2.9999...×10

=> 10x = 29.9999...----(2)

On Subtracting (1) from (2) then

10x = 29.999...

x = 2.999...

(-)

____________

9x = 27.000...

___________

=> 9x = 27

=>x = 27/9

=> x = 3

So, 2.9(bar on 9) = 3

We know that

The irrational number between a and b is √(ab)

We have a = 3 , b = 3

The irrational number = √(3×3) = 3

Answer :-

2.998877654321... by method-1

(We can write so many numbers with Non terminating and non recurring decimal)

3 by method-2

(Since the given numbers are same.)

Used formulae:-

• The irrational number between a and b is √(ab)
• Non terminating and non recurring decimal is an irrational number.
• There are infinitely number of many irrational numbers between two numbers is called Densitive Property.