Question

Express the number 0.245(45 bar) in the form of p+q, where p and q are integers, q is not equal to zero.

Answer 1

0.245454545.......
Periodicity( no of numbers repeating) = 2
Let x=0.2454545.....
As periodicity is 2 we should multiply x with 100 on both sides
100x= 24.54545..
(-)  x=   0.24545..
______________
  99x= 24.30000....

Now 99x= 243/10 
            x= 243/10*90
            x=243/90= 81/30=27/10  [ cancellation with 3]
     Therefore 0.2454545..=27/10

Answer 2

Answer:

The required form is $x=\frac{27}{110}$

Step-by-step explanation:

Given : Expression $0.245(45\text{ bar})$

To find : Express expression in the p/q form where p and q are integers, q is not equal to zero.?

Solution :

Let $x=0.2454545...$ ....(1)

Multiply both side by 100,

$100x=24.54545...$ .....(2)

Subtract (1) and (2),

$100x-x=(24.54545....)-(0.2454545....)$

$99x=24.3$

$x=\frac{24.3}{99}$

$x=\frac{243}{990}$

$x=\frac{27}{110}$

Therefore, The required form is $x=\frac{27}{110}$