To find the total weight of the dump truck after adding 15,300 pounds of trash, you can add the weight of the empty truck to the weight of the trash.
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The weight of the empty dump truck is: \[ 2.8 \times 10^5 \text{ pounds} \]
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The weight of the trash is: \[ 15,300 \text{ pounds} \] To express 15,300 in scientific notation: \[ 15,300 = 1.53 \times 10^4 \text{ pounds} \]
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Now, we need to add the two weights. Before we can add them, it helps to express both in the same format. We can convert \(2.8 \times 10^5\) to a common exponent: \[ 2.8 \times 10^5 = 28.0 \times 10^4 \]
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Now we can add this to \(1.53 \times 10^4\): \[ 28.0 \times 10^4 + 1.53 \times 10^4 = (28.0 + 1.53) \times 10^4 = 29.53 \times 10^4 \]
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Finally, we convert \(29.53 \times 10^4\) into proper scientific notation: \[ 29.53 \times 10^4 = 2.953 \times 10^5 \]
Thus, the total weight of the dump truck after adding the trash is: \[ \boxed{2.953 \times 10^5} \text{ pounds} \]
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