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Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.
Given:
Given rational numbers are $\frac{5}{7}$ and $\frac{9}{11}$.
To do:
We have to find three irrational numbers between the given numbers.
Solution:
A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.
We can insert infinite irrational numbers between two rational numbers.
$\frac{5}{7} = 0.7142857…..$
$\frac{9}{11} = 0.81818……$
Therefore,
$0.72644513…., 0.736546…., 0.7465664…$ are less than $\frac{5}{7} = 0.7142857…..$ and greater than $\frac{9}{11} = 0.81818……$.
Three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$ are $0.72644513…., 0.736546….$ and $0.7465664…$.
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