To find the total weight of the dump truck after adding 15,300 pounds of trash, we need to add the weight of the empty dump truck (2.8 × 10^5 pounds) to the weight of the trash (15,300 pounds).
First, we can convert 15,300 pounds into scientific notation.
15,300 = 1.53 × 10^4 pounds.
Now, we'll add the weights. To add them in scientific notation, we need them to have the same exponent:
We rewrite \(2.8 × 10^5\) as \(28 × 10^4\) (by multiplying 2.8 by 10, we move the decimal one place to the right and decrease the exponent by 1).
Now we can add:
\[ 28 × 10^4 + 1.53 × 10^4 = (28 + 1.53) × 10^4 = 29.53 × 10^4 \]
Now, we convert \(29.53 × 10^4\) to standard scientific notation:
\[ 29.53 × 10^4 = 2.953 × 10^5 \text{ (moving the decimal one place to the left increases the exponent by 1)} \]
So the total weight of the dump truck with the trash added is:
\[ \text{Total weight} = 2.953 × 10^5 \text{ pounds.} \]
Thus, the final answer is:
2.953 × 10^5 pounds.