Question

If p and q are integers with q is not equal to 0 then express 121.111... In p/q form

Answer 1

Question :

Express 121.111 ... in p/q form , where q ≠ 0

Solution :

Let , x = 121.111 .... --- (i)

Multiply eq (i) by 10 , we get

10x = 1211.111 .... --- (ii)

Subtract eq (i) from eq (ii) , we get

$\sf \Rightarrow 10x - x = 1211.111 .... - 121.111 .... \\ \\ \sf \Rightarrow </p><p>9x = 1090 \\ \\ \sf \Rightarrow </p><p>x = \frac{1090}{9}$

$\therefore \bold{ \sf \underline{121. \bar{1} \: can \: be \: written \: as \: \frac{1090}{9} \: \: }}$