Question

express the following rational number in the form of p\q,where q and p are integer and q ≠0
1)0.2777777777777777.......​

Answer 1

Answér :

0.2777... = 5/18

Solution :

Here ,

We need to express 0.2777.... in the form of p/q where p and q are integers and q≠0 .

Thus ,

Let X = 0.2777.... --------(1)

Now ,

Multiplying both the sides of eq-(1) by 10 ,

We have ;

=> 10 × X= 10 × 0.2777....

=> 10X = 2.777.... ---------(2)

Now ,

Multiplying both the sides of eq-(2) by 10 ,

We have ;

=> 10 × 10X = 10 × 2.777....

=> 100X = 27.777.... -------(3)

Now ,

Subtracting eq-(2) from (3) , we get ;

=> 100X - 10X = 27.777.... – 2.777....

=> 90X = 25

=> X = 25/90

=> X = 5/18

=> 0.2777.... = 5/18

Hence ,

0.2777.... = 5/18