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# Find three different irrational numbers between the rational numbers 5/ 7 and 9 /11.

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

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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 $\dpi{80} \frac{5}{7}$ and $\dpi{80} \frac{9}{11}$  are

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

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