Question

What is the decimal representation of 5/11

Answer 1

0.45 is the answer but
0.45454545454is it

Answer 2

`(5)/(11)=0.\overline{45}`

Explanation:

Given:
`(5)/(11)`

We need to change given fraction into decimal.

`x=(5)/(11)-------(1)`

`11x=5`

Multiply both sides by 9

`99x=45-----------(2)`

Add equation (1) and (2)

`99x+x=45+(5)/(11)`

`100x=45.45.....`

Divide both sides by 100

`x=0.454545.....`

`(5)/(11)=0.454545.......=0.\overline{45}`