To find the total weight of the dump truck after adding the trash, you can add the weight of the empty truck to the weight of the trash:
- Weight of the empty dump truck = \( 2.8 \times 10^5 \) pounds
- Weight of the trash = 15,300 pounds
First, convert 15,300 pounds to scientific notation:
15,300 = \( 1.53 \times 10^4 \) pounds.
Now, we add the two weights. To do this effectively, it's preferred to express both numbers with the same power of ten. To do this, we can convert \( 2.8 \times 10^5 \) into a form that allows us to add it to \( 1.53 \times 10^4 \).
Converting \( 1.53 \times 10^4 \) to have the same exponent as \( 2.8 \times 10^5 \):
\[ 1.53 \times 10^4 = 0.153 \times 10^5 \]
Now, we can add the two weights together:
\[ 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 \]
Calculating the sum:
\[ 2.8 + 0.153 = 2.953 \]
So:
\[ 2.953 \times 10^5 \text{ pounds} \]
Thus, the total weight of the dump truck with trash in scientific notation is:
2.953 × 10^5 pounds.