Question

The representation of 0.9^bar as a rational number is

Answer 1

Given:

• 0.9

To Find:

• The representation of 0.9 as a rational number

Solution:

➞ Let x = 0.9 (0.999)

➞ 10x = 9.999

➞ 10x - x = 9.999, - 0.999

➞ 9x = 9

➞ x = 9/9 = 1

Hence,

• The representation of 0.9 as a rational number is 1

______________

Answer 2

Given data: 0.9 bar

To find:  $\frac{p}{q}$ form

Solution:

Bar is the continuous number without termination.

Now we need to get $\frac{p}{q}$ form, Let x = 0.99999...

=> 10x = 9.9999...

=> 10x = 9 + 0.999...

=> 10x = 9 + x (0.9 bar is considered as x)

=> 10x - x = 9

=> 9x = 9

=> x = 1

Hence the representation of 0.9 bar as a rational number is 1.