To find the total weight of the dump truck when 15,300 pounds of trash is added, we add the weight of the empty dump truck to the weight of the trash:
\[ \text{Weight of empty dump truck} = 2.8 \times 10^5 \text{ pounds} \] \[ \text{Weight of trash} = 15,300 \text{ pounds} = 1.53 \times 10^4 \text{ pounds} \]
Now, we need to add these two weights together:
\[ 2.8 \times 10^5 + 1.53 \times 10^4 \]
To do this, we first need to express \(1.53 \times 10^4\) in the same power of ten as \(2.8 \times 10^5\). We can do this by converting \(1.53 \times 10^4\) to a power of ten that matches \(10^5\):
\[ 1.53 \times 10^4 = 0.153 \times 10^5 \]
Now we can add the two values:
\[ 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 \] \[ = 2.953 \times 10^5 \]
Thus, the total weight of the dump truck with the added trash is \(2.953 \times 10^5\) pounds.
In scientific notation, the final answer is:
\[ \boxed{2.953 \times 10^5} \] pounds.