Look Up a Table of Physical Constants and Determine the Value of This Ratio. What Does Exercise Chapter 1 Electric

Question 3: Check that the ratio ke²/G m_em_p is dimensionless. Look up a Table of physical constants and determine the value of this ratio. What does the ratio signify?
Solution:
Use the table of physical constants we get
Unit of
G  = N m² kg⁻².
me = Kg
mp = Kg       (Masses of electron and proton)
e = C           (e is electric charge)
k = 1/4πε₀  = Nm²C^-2
Plug the values of the units, we get

= N⁰m⁰C⁰Kg⁰

All units have canceled out hence it is a ratio, because ratio has no unit 

Values of all variable or constant 
Charge in electron , e = 6 × 10⁻¹⁹ C
Gravitational constant G = 6.67 × 10−11 N m² kg^-2
Mass of electron, m_e= 9.1 × 10⁻³¹ kg
Mass of proton , m_p = 1.66 × 10⁻²⁷ kg
Plug the values

Ratio is nearly equal to 2.3 × 10 ³⁹.