Question

find an irrational number between 5/7 and 7/9 how many more there may be?

Answer 1

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5/7 = 0.7111
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7/9 = 0.77

We have to find an irrational number between 0.711... and 0.777...
Decimal expansions of irrational numbers would be non-terminating non-repeating expansions.
Such a number between the given two numbers is 0.7123456....
There are infinitely many irrational numbers between the given two numbers.