An empty dump truck weighs about 2.8×105 pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.(1 point)

Question

Responses

29,530 pounds
29,530 pounds

15,302.8 pounds
15,302.8 pounds

4.33×105 pounds
4.33 times 10 superscript 5 baseline pounds

2.953×105 pounds

Answer 1

To find the total weight of the dump truck when 15,300 pounds of trash is added, we can sum the weight of the empty dump truck and the weight of the trash:

1. Weight of empty dump truck = \( 2.8 \times 10^5 \) pounds
2. Weight of trash = 15,300 pounds

Now, we convert 15,300 pounds to scientific notation:

15,300 can be expressed as \( 1.53 \times 10^4 \) pounds.

Now, we add the two weights together (converting \( 2.8 \times 10^5 \) to have the same order of magnitude as \( 1.53 \times 10^4 \)):

First, we can express \( 1.53 \times 10^4 \) in terms of \( 10^5 \):

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

Now, we can add the two weights:

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

Thus, the total weight of the dump truck with trash is \( 2.953 \times 10^5 \) pounds.

Therefore, the correct answer in scientific notation is:

2.953×10^5 pounds.