Observe that
[tex]\dfrac{23}{11}=\dfrac{22+1}{11}=\dfrac{22}{11}+\dfrac{1}{11}=2+\dfrac{1}{11}[/tex]
Since 1/11 has the decimal expansion
[tex]0.\overbar{09}[/tex]
The fraction is equivalent to
[tex]\dfrac{23}{11}=2.\overbar{09}[/tex]
Decimal equivalent of fraction [tex]\frac{23}{11}[/tex] is [tex]\bold{2 . \overline{09}}[/tex]
Solution:
Need to determine decimal equivalent to [tex]\frac{23}{11}[/tex]
On rewriting fraction [tex]\frac{23}{11}[/tex] , we get
[tex]\frac{23}{11}=\frac{22}{11}+\frac{1}{11}[/tex]
[tex]=>\frac{23}{11}=2+\frac{1}{11} \rightarrow(1)[/tex]
On using long division method to calculate [tex]\frac{1}{11}[/tex] we get
[tex]1 \div 11=0.0909090909 \ldots[/tex]
So from equation (1), we get
[tex]\frac{23}{11}=2+0.0909090 \ldots=2.09090909=2 . \overline{09}[/tex]
Hence decimal required is [tex]2 . \overline{09}[/tex]
