 Intersection formula for blowing up a surface

If $\pi :\tilde{X}\to X$ blows up a smooth point with exceptional curve $E$, thenIf a curve $C$ has multiplicity $m$ at the center, its strict transform is $\tilde{C}={\pi }^{\ast }C-mE$ and ${\tilde{C}}^2=C^2-m^2$.