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)

Question

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