an empty dump truck weighs about 2.8×10 to the fifth power pounds how much does it weigh if 15,300 pounds of trash is at it. The answer should be in scientific notation.

Answer 1

To determine the total weight of the dump truck when it is loaded with trash, you can simply add the weight of the empty dump truck to the weight of the trash.

The weight of the empty dump truck is: \[ 2.8 \times 10^5 \text{ pounds} \]

The weight of the trash is: \[ 15,300 \text{ pounds} \]

First, we need to express \( 15,300 \) in scientific notation: \[ 15,300 = 1.53 \times 10^4 \text{ pounds} \]

Now, we can add the two weights together. However, to add them, it's easier to convert the first term to the same power of ten as the second term.

Convert \( 2.8 \times 10^5 \) to: \[ 2.8 \times 10^5 = 28 \times 10^4 \]

Now we can add: \[ (28 \times 10^4) + (1.53 \times 10^4) = (28 + 1.53) \times 10^4 = 29.53 \times 10^4 \]

Next, we convert \( 29.53 \times 10^4 \) to standard scientific notation: \[ 29.53 \times 10^4 = 2.953 \times 10^5 \]

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