Question

If a real number is written as 1.18181818…. Write its \(a\over b\) form
1. \(16\over11\)
2. \(13\over11\)
3. \(18\over17\)
4. \(19\over17\)

Answer 1

Correct Answer - Option 2 : \(13\over11\)

Calculation:

Given real number is 1.181818….

Let x = 1.18181818…… as two digits are repeating, lets multiply x by 100,

⇒ 100x = 118.181818….

⇒ 100x – x = 118.181818…. – 1.181818…

⇒ 99x = 117

⇒ x = \(13\over11\)