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 with the added trash, you can add the weight of the empty truck and 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, let's convert 15,300 pounds into scientific notation: \[ 15,300 = 1.53 \times 10^4 \text{ pounds} \]

Now add the two weights together: \[ 2.8 \times 10^5 + 1.53 \times 10^4 \] To add these, we need to 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: \[ 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 = 2.953 \times 10^5 \text{ pounds} \]

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