Question

Express the following in the form p/q, where p and q are integers and q ≠ 0.

(i)  \(0. \bar { 3 } \)

(ii) \(0.\overline{47}\)

(iii) 1.23

(iv) \(1.2\overline{35}\)

Answer 1

(i)  \(0. \bar { 3 } \)

Let x = \(0. \bar { 3 } \)

i.e., x = 0.3333 …(i)

Multiplying (i) by 10, we get

10x = 3.3333 …(ii)

Subtracting (i) from (ii),

we get 10x – x = 3.3333… – 0.3333…

⇒ 9x = 3

⇒ x = 3/9

⇒ x = 1/3

(ii) \(0.\overline{47}\)

(iii) 1.23

= 1.272727 ......(i)

Multiplying (i) by 100, we get

100x = 127.2727

Subtracting (i) from (ii), we get

 99x = 126

⇒ x = 126/99 = 14/11

(iv) \(1.2\overline{35}\)