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)
Responses
15,302.8 pounds
15,302.8 pounds
29,530 pounds
29,530 pounds
2.953×10^5 pounds
2.953 times 10 superscript 5 baseline pounds
4.33×10^5 pound
To find out how much the dump truck weighs after adding 15,300 pounds of trash, we simply need to add the weight of the trash to the weight of the empty truck.
The empty truck weighs: \(2.8 \times 10^5\) pounds
The trash weighs: 15,300 pounds (which can also be written as \(1.53 \times 10^4\) pounds in scientific notation)
Now we add the two weights together:
\((2.8 \times 10^5) + (1.53 \times 10^4)\)
Since the weights are given in different orders of magnitude, we need to express them with the same exponent of 10 for easier addition. We can express \(1.53 \times 10^4\) as \(0.153 \times 10^5\) to match the order of magnitude of the truck's weight.
Now, add them together:
\((2.8 \times 10^5) + (0.153 \times 10^5) = (2.8 + 0.153) \times 10^5 = 2.953 \times 10^5\)
Therefore, the weight of the truck after adding the trash is \(2.953 \times 10^5\) pounds.