An empty dump truck weighs about 2.8 x 10 to the fifth power pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.

Answer 1

To find the total weight of the dump truck after adding the trash, you need to add the weight of the empty dump truck to the weight of the trash:

1. The weight of the empty dump truck is \( 2.8 \times 10^5 \) pounds.
2. The weight of the trash is \( 15,300 \) pounds, which can also be expressed in scientific notation: \( 1.53 \times 10^4 \) pounds.

Now, you can add these two weights together. However, it's helpful to express both numbers in the same powers of ten. To add them, convert \( 1.53 \times 10^4 \) to a form that aligns with \( 10^5 \):

\[ 1.53 \times 10^4 = 0.153 \times 10^5 \]

Now add the two amounts:

\[ 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 = 2.953 \times 10^5 \]

Finally, express \( 2.953 \times 10^5 \) in scientific notation. It’s already in proper form because \( 2.953 \) is between 1 and 10.

Thus, the total weight of the dump truck with the trash added is:

\[ \boxed{2.953 \times 10^5} \text{ pounds} \]