To calculate the total dinner bill including a 20% gratuity, you would follow these steps:
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Calculate the gratuity: \[ \text{Gratuity} = \text{Dinner Bill} \times \text{Gratuity Rate} \] \[ \text{Gratuity} = 64.83 \times 0.20 = 12.966 \]
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Round the gratuity to the nearest cent: \[ \text{Gratuity} \approx 12.97 \]
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Calculate the total bill including the gratuity: \[ \text{Total} = \text{Dinner Bill} + \text{Gratuity} \] \[ \text{Total} = 64.83 + 12.97 = 77.80 \]
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Round to the nearest hundred: Since $77.80 is closer to $100 than it is to $0, rounding to the nearest hundred would give $100.
Thus, the total for the Jones family dinner, including a 20% gratuity rounded to the nearest hundred, is $100.