Here's our best estimate: 8904 dimes.
Dime, the smallest, thinnest coin in use today has the following specifications:
Weight: 2.268 g
Diameter: 0.705 in (17.91 mm)
Thickness: 1.35 mm
Get the volume of the dime using the formula: VOLUME = π * (radius)² * height
Plug in the numbers:
V = 3.14159 * (8.955 mm)² * 1.35 mm
V = 3.14159 * 80.192025 mm * 1.35 mm
V = 340.10641343226 mm³
We know that 1 gallon = 3785412 mm³ - Metric-Conversions.org
Now, divide the volume of the jug by the volume of a dime:
3785412 mm³ / 340.10641343226 mm³
But since they don't fit in perfectly, you are really looking at less. Upon estimation, they pack about 80% efficiently.
Now, divide your estimate for the volume of a penny into 80% of the volume of the jug.
80% of 3785412 mm³ = 3028329.6 mm³
3028329.6 mm³ / 340.10641343226 mm³
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