Question

Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.

Answer 1

Let us convert $\frac{5}{7}$ and $\frac{9}{11}$ into decimal form, to get

$\frac{5}{7}=\mathrm{0.714285...}$ and $\frac{9}{11}=\mathrm{0.818181....}$

We know that the Non-terminating non-recurring decimals are irrational numbers.

Three irrational numbers that lie between $\mathrm{0.714285....}$ and $\mathrm{0.818181....}$ are:

$0.73073007300073\dots .$

$0.74074007400074\dots .$

$\mathrm{0.76076007600076.....}$