Question

Which decimal is equivalent to the fraction 23/11

Answer 1

Observe that

`(23)/(11)=(22+1)/(11)=(22)/(11)+(1)/(11)=2+(1)/(11)`

Since 1/11 has the decimal expansion

`0.\overbar{09}`

The fraction is equivalent to

`(23)/(11)=2.\overbar{09}`

Answer 2

Decimal equivalent of fraction
`(23)/(11)` is
`\bold{2 . \overline{09}}`

Solution:

Need to determine decimal equivalent to
`(23)/(11)`

On rewriting fraction
`(23)/(11)` , we get

`(23)/(11)=(22)/(11)+(1)/(11)`

`=>(23)/(11)=2+(1)/(11) \rightarrow(1)`

On using long division method to calculate
`(1)/(11)` we get

`1 / 11=0.0909090909 \ldots`

So from equation (1), we get

`(23)/(11)=2+0.0909090 \ldots=2.09090909=2 . \overline{09}`

Hence decimal required is
`2 . \overline{09}`