Question

Express 0.4191919 in the form of p/q where p and a are integers and q is not equal to zero ( step by step)

Answer 1

Given, the expression 1.4191919...

Let 1.4191919....=x  ⟹(i).

Multiplying (i) by 10,

⟹14.191919....=10x  ⟹(ii).

Multiplying (ii) by 1000,

⟹1419.191919....=1000x  ⟹(iii).

Then, (iii)−(ii)

⟹ 1000x−10x=1419.191919....−14.191919....

⟹ 990x=1405

⟹x=

990

1405

​

=

198

281

​

.

Hencs, 1.4191919... in  

q

p

​

 is  

198

281

​

.