The given ratio is $\frac{k{e}^2}{G{m}_e{m}_p}$ Where G= Gravitational constant. Its unit is $N{m}^{2}k{g}^{-2}$
${\mathrm{m}}_{\mathrm{e}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{m}}_{\mathrm{p}}$ = Masses of electron and proton and their unit is kg.
e = Electric charge. Its unit is C.
$k=\frac{1}{4\pi {\epsilon }_0}\text{\hspace{0.17em}and its unit is\hspace{0.17em}}N{m}^2{C}^{-2}$
Therefore, the unit of the given ratio
$\frac{k{e}^2}{G{m}_e{m}_p}=\frac{\left[N{m}^2{C}^{-2}\right]\left[C^{-2}\right]}{\left[N{m}^{2}k{g}^{-2}\right]\left[kg\right]\left[kg\right]}=M^0{L}^0{T}^0$
Hence, the given ratio is dimensionless. WAR
$\begin{array}{l}e=1.6\times {10}^{-19}C\\ G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}\\ m_e=9.1\times {10}^{-31}kg\\ m_p=1.66\times {10}^{-27}kg\end{array}$
Hence, the numerical value of the given ratio is
$\frac{k{e}^2}{G{m}_e{m}_p}=\frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{6.67\times {10}^{-11}\times 9.1\times {10}^{-31}\times 1.67\times {10}^{-27}}\approx 2.3\times {10}^{39}$
This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.