Factor $490=7^{2}\times 10$. Rewrite the square root of the product $\sqrt{7^{2}\times 10}$ as the product of square roots $\sqrt{7^{2}}\sqrt{10}$. Take the square root of $7^{2}$.
$$\frac{1}{111111111\times 7\sqrt{10}}$$
Multiply $111111111$ and $7$ to get $777777777$.
$$\frac{1}{777777777\sqrt{10}}$$
Rationalize the denominator of $\frac{1}{777777777\sqrt{10}}$ by multiplying numerator and denominator by $\sqrt{10}$.
