Question

Express 0.9 bar inform p/q where where p and q are integer

Answer 1

Let,
x=0.9bar
x=0.999....... (1)
10x=9.999......... (2)
On Subtracting (1) from (2) ,
10x= 9.999.........
- x= 0.999.........
________________
9x=9
x=9/9 i.e in the form of p/q.

Answer 2

Given:

Number = $0.\overline{9}$

To find:

The $\dfrac{p}{q}$ form of given number, where p and q are integer.

Solution:

Let, $x=0.\overline{9}$

$x=0.999...$        ...(i)

Multiply both sides by 10.

$10x=9.999...$       ...(ii)

Subtracting (i) from (ii), we get

$10x-x=9.999...-0.999...$  

$9x=9$

Divide both side by 9.

$x=1$

So, $0.\overline{9}\approx 1$.

Therefore, when we convert $0.\overline{9}$ in$\dfrac{p}{q}$ form we get $\dfrac{1}{1}=1$.