An empty dump truck weighs about 2.8×10^5

Question

pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.(1 point)
Responses

15,302.8 pounds
15,302.8 pounds

29,530 pounds
29,530 pounds

4.33×105
pounds
4.33 times 10 superscript 5 baseline pounds

2.953×10^5
pounds

Answer 1

To find the total weight of the dump truck when 15,300 pounds of trash is added, you can add the weight of the empty dump truck to the weight of the trash:

1. Weight of the empty dump truck: \(2.8 \times 10^5\) pounds
2. 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, we can add the two weights. However, it’s easier to express them in the same power of ten:

\[ 2.8 \times 10^5 \text{ pounds} = 280,000 \text{ pounds} \] \[ 15,300 \text{ pounds} = 0.153 \times 10^5 \text{ pounds} \]

Now, we can add:

\[ 280,000 + 15,300 = 280,000 + 15,300 = 295,300 \text{ pounds} \]

In scientific notation, \(295,300\) can be expressed as:

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

Therefore, the total weight of the dump truck with the trash added is:

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