Question

an empty dump truck weighs about 2.8×10 to the power of 5th 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 15,300 pounds of 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 be converted to scientific notation.

To convert 15,300 to scientific notation:

\[
15,300 = 1.53 \times 10^4 \text{ pounds}
\]

Now, we can add the weights together:

\[
Total\,Weight = 2.8 \times 10^5 + 1.53 \times 10^4
\]

To add these two values, it's easier if both numbers are in the same power of ten. We can rewrite \( 1.53 \times 10^4 \) in terms of \( 10^5 \):

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

Now we can add them:

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

Thus, the total weight of the dump truck after adding the trash is:

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