An empty dump truck weighs about 2.8×10 to the power of 5 pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.

Answer 1

To find the weight of the dump truck after adding the trash, you need to add the weight of the empty dump truck to the weight of the trash.

The empty dump truck weighs: \[ 2.8 \times 10^5 \text{ pounds} \]

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

First, convert 15,300 pounds into scientific notation: \[ 15,300 = 1.53 \times 10^4 \text{ pounds} \]

Now, add the weights together:

1. First convert \( 2.8 \times 10^5 \) to have the same exponent: \[ 2.8 \times 10^5 = 2.8 \times 10^5 \text{ pounds} \] Since \( 10^5 \) is larger than \( 10^4 \), we can express \( 1.53 \times 10^4 \) with the same exponent as \( 10^5 \). This means: \[ 1.53 \times 10^4 = 0.153 \times 10^5 \]

Now we can add: \[ 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 = 2.953 \times 10^5 \]

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