Q.Suppose unknowingly you wrote the universal gravitational constant value as $G = 6.67\times10^{11}$ instead of the correct value $G = 6.67\times10^{-11}$, what is the acceleration due to gravity $g'$ for this incorrect $G$? According to this new acceleration due to gravity, what will be your weight $W'$?

$G$, the universal gravitational constant, is the fixed number that sets exactly how strong gravity is between any two given masses at any given separation. Its accepted modern value is

first measured experimentally by Henry Cavendish in 1798 using a delicate torsion balance, who obtained $G\approx6.75\times10^{-11}\ \text{N m}^2\text{kg}^{-2}$ -- remarkably close to today's accepted value, using 18th-century equipment.

Why $G$ being so small matters. Because $G$ is such a tiny number, the gravitational force between two ordinary, human-scale masses is utterly negligible (a fraction of a newton even at close range) -- which is precisely why we never feel any gravitational pull from nearby people or objects. Gravity only becomes a dominant, easily-felt force once one of the two masses involved is planet-sized, because the huge mass compensates for the smallness of $G$. …