Question

Solve Q3. Proper explanation and complete steps

Answer 1

Question

Express $\sf 0.\overline{253}$ as a fraction in the simplest form.

Solution

Let, 0.253253253... = x in its p/q form

Multiplying 1000 on both sides, we get

⇒ 1000x = 253.253253.....

(here we multiplied with 1000 because repetition was of three digits)

Now, subtract x from 1000x

⇒ 1000x - x = $\sf 253.\overline{253} - 0.\overline{253}$

⇒ 999x = 253

⇒ x = 253/999

Now, we can not simplify it further, hence the simplest form of fraction of $\sf 0.\overline{253}$ would be 253/999.