Question

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

Answer 1

Decimal expansion of,

1. $\frac{5}{7} = 0. \overline{714285}$.
2. $\frac{7}{9} = 0. \overline{7}$.

Easily, we can get,

• $0.75775777577775...$
• $0.767667666...$
• $0.744447744444444...$.

There are infinitely (∞) many irrational numbers between any two rational numbers.

More:-

• An irrational number has a non terminating, non repeating decimal expansion.
• A few popular irrational constants:-

1. $\pi$ (Pi constant)
2. $ϕ$ (The golden ratio),
3. $e$ (Euler’s number), etc.