Question

..express 18.742 in p/q form then find p+q​

Answer 1

Answer:

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

.