We know that the acceleration due to gravity acting on a body situated h meter away from the surface of the earth is given by,
$$g' = (1 - 2h/r)g,$$ where $\,r$ = Radius of the earth ($R$) + $h$. Now we can find the range of the earth's gravitational field, i.e, where does the value of g' become $0$.
Now, $g'$ becomes $0\,$ if $\,h = R/ 2$. Radius of the earth = $6.37\cdot10^6$ m, so $R/ 2 = 3.18\cdot10^6$ m. Therefore, at a distance $3.18\cdot10^6$ m distance away from the surface of the earth, the gravitational field of the earth becomes zero or the value of $g$ becomes zero. Is my math correct? If not, why?