Question

Find an irrational number between $\frac{5}{7}$ and $\frac{7}{9}$. How many more there may be?

Answer 1

Now,

$\frac{5}{7}=\mathrm{0.7142857.............}$
$\frac{7}{9}=\mathrm{0.7777777777777.........}$
We know that irrational numbers are numbers whose decimal representation is non terminating and non repeating.

Also, between two rational numbers, there exists infinite irrational numbers. Therefore, an irrational number between $\frac{5}{7}$ and $\frac{7}{9}$ can be,

$\mathrm{0.723472334472333444..}$ or $\mathrm{0.757755777555...}$ or $\mathrm{0.760760076000...}$ and so on.