8. Find three different irrational numbers between the rational numbers \frac{5}{7} and \frac{9}{11} .

Answers (1)

We can write  \frac{5}{7}  as 

\Rightarrow \frac{5}{7} = 0.714285714285.... = 0.\overline{714285}

And  \frac{9}{11} as 

\Rightarrow \frac{9}{11} = 0.818181.... = 0.\overline{81}
Therefore,  three different irrational numbers between the rational numbers \frac{5}{7} and \frac{9}{11}  are 

1) 0.72737475....
2) 0.750760770780...
3) 0.790780770760....

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