Rationalise the denominator of $\frac{1}{\sqrt{2}}$.

We want to write $\frac{1}{\sqrt{2}}$ as an equivalent expression in which the denominator is a rational number. We know that $\sqrt{2} \cdot \sqrt{2}$ is rational. We also know that multiplying $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ will give us an equivalent expression, since $\frac{\sqrt{2}}{\sqrt{2}}=1 .$ So, we put these two facts together to get

$\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

In this form, it is easy to locate $\frac{1}{\sqrt{2}}$ on the number line. It is half way between $0$ and $\sqrt{2}$.