Question

An empty dump truck weighs about 2.8×10^5 pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.(1 point)
Responses

29,530 pounds
29,530 pounds

15,302.8 pounds
15,302.8 pounds

2.953×10^5 pounds
2.953 times 10 superscript 5 baseline pounds

4.33×10^5 pounds

Answer 1

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

1. The weight of the empty dump truck: \( 2.8 \times 10^5 \) pounds
2. The weight of the trash: 15,300 pounds

First, convert 15,300 pounds to scientific notation:
\[
15,300 = 1.53 \times 10^4 \text{ pounds}
\]

Now you will need to add \( 2.8 \times 10^5 \) pounds and \( 1.53 \times 10^4 \) pounds. It's easiest to express both quantities with a common order of magnitude:

Convert \( 1.53 \times 10^4 \) to an equivalent in terms of \( 10^5 \):
\[
1.53 \times 10^4 = 0.153 \times 10^5 \text{ pounds}
\]

Now add these two quantities:
\[
2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 = 2.953 \times 10^5 \text{ pounds}
\]

Thus, the total weight of the dump truck after adding the trash is:
\[
\boxed{2.953 \times 10^5 \text{ pounds}}
\]