First we need to find some commonalities between the gumball and the jar. Both the gumball and the jar can be converted into cubic inches.
The formula for finding the volume of a sphere is V = 4/3piR³
Assuming the 1" dimension is the diameter of the gumball.
V = 4/3pi(½)³
v = 4/3 x 3.14 x (1/2)^3
v = 4/3 x 3.14 x .125 = 0.52 cubic inches
Also assuming the interior of the jar is one gallon then using a conversion chart we can find that one gallon is equal to 231 cubic inches.
We could divide 231 by .52 to get roughly 444, however this does not account for the empty space between each gumball. For estimating, we will assume that each 1 inch gumball with the surrounding empty space is equal to 1 cubic inch. Therefore, in a 1 gallon jar which will hold 231 cubic inches will hold 231 gumballs.