The number 0.1235235235 in the $$\frac{p}{q}$$​ form is equal to:

Correct option is C

​Given:

The number 0.1235235235...

Solution:

Let x = 0.1235235235...

Multiply by 100, we have

100x = 12.35235235...

We multiply by 10³ = 1000.

1000 $$\times$$​ (100x) = 1000 $$\times$$ (12.35235235...)

100000x = 12352.35235235...

Now,

100000x - 100x = 12352.35235235... - 12.35235235...

99900x = 12340

x =$$\frac{ 12340 }{ 99900}$$ = $$\frac {617}{4995}$$

Alternate Method:

Number 0.1$$\overline {235}$$

Concept Used:

$$0.a\overline {bcd}= \frac{abcd -a}{9990}$$

Solution:

0.1$$\overline {235}$$

= $$\frac{1235-1}{9990}= \frac{1234}{9990}=\frac {617}{4995}$$​​