Question

Express 0.23 (bar) in the form of p/q

Answer 1

`0.\overline{23}= (23)/(99)`

Explanation:

Let
`x = 0.\overline{23}`....(1)

Multiply both sides by 100.

`100x = 23.\overline{23}`....(2)

Subtracting equation (1) from equation (2)

`100x -x= 23.\overline{23}-0.\overline{23}`

`\implies 99x= 23`

`\implies x= (23)/(99)`

`\implies\huge{\orange{ 0.\overline{23}= (23)/(99)}}`