# Find three different irrational numbers between the rational numbers

Question:

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

Solution:

Let $x=\frac{5}{7}=0 . \overline{714285}$ and $y=\frac{9}{11}=0 . \overline{81}$

Here we observe that in the first decimal x has digit 7 and y has 8. So x < y. In the second decimal place x has digit 1. So, if we considering irrational numbers

$a=0.72072007200072 \ldots$

$b=0.73073007300073 \ldots$

$c=0.74074007400074 \ldots$

We find that

\$x

Hence  are required irrational numbers.