Find three different irrational numbers between the rational numbers $\frac{1}{4}$ and $\frac{4}{5}$.

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We know $\frac{1}{4}=0.25$ and $\frac{4}{5}=0.8$

So, to find three different irrational numbers between $\frac{1}{4}$ and $\frac{4}{5},$ we find three different irrational numbers between $0.25$ and $0.8$ which are non-terminating and non-recurring. Three such numbers are

$0.30300300030000 \ldots$

$0.40400400040000 \ldots$

$0.50500500050000 \ldots$

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