To find the savings from purchasing a 128-ounce jug of milk instead of two 64-ounce cartons, we can perform the following calculations:
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Calculate the total cost of the 128-ounce jug: \[ \text{Cost of 128-ounce jug} = 128 , \text{ounces} \times 0.048 , \text{dollars/ounce} = 128 \times 0.00048 = 0.06144 , \text{dollars} = 6.144 , \text{dollars} \]
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Calculate the cost of one 64-ounce carton: \[ \text{Cost of one 64-ounce carton} = 64 , \text{ounces} \times 0.051 , \text{dollars/ounce} = 64 \times 0.00051 = 0.03264 , \text{dollars} = 3.264 , \text{dollars} \]
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Calculate the total cost for two 64-ounce cartons: \[ \text{Cost for two 64-ounce cartons} = 2 \times 3.264 = 6.528 , \text{dollars} \]
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Now, calculate the savings: \[ \text{Savings} = \text{Cost of two cartons} - \text{Cost of one jug} = 6.528 - 6.144 = 0.384 , \text{dollars} \]
The savings are approximately $0.38.
Therefore, the answer is:
\[ \boxed{0.38} \]