Question

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

Answer 1

Let a = $\frac{5}{7}$ = 0.714285714285 = 0.$\overline{714285}$

and b = $\frac{9}{11}$ = 0.8181... = 0.$\overline{81}$

We see that a has six digits and b has two digits, i.e. 0.71 < 0.81

$\therefore$ $\frac{5}{7}<\frac{9}{11}$

$\therefore$ First irrational number

will be 0.72020020002....

and 0.74020020002....

and 0.76020020002....