An empty dump truck weighs about 2.8×105 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 2.953×105 pounds 2.953 times 10 superscript 5 baseline pounds 4.33×105 pounds

Answer 1

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

Weight of the empty dump truck = \( 2.8 \times 10^5 \) pounds
Weight of the trash = 15,300 pounds

First, we convert 15,300 pounds to scientific notation:

15,300 = \( 1.53 \times 10^4 \) pounds

Now we can add the two weights:

\[ 2.8 \times 10^5 + 1.53 \times 10^4 \]

Since \( 10^5 \) is larger than \( 10^4 \), we need to convert \( 1.53 \times 10^4 \) to match the exponent of \( 10^5 \):

\[ 1.53 \times 10^4 = 0.153 \times 10^5 \]

Now we can add the weights:

\[ 2.8 \times 10^5 + 0.153 \times 10^5 = (2.8 + 0.153) \times 10^5 = 2.953 \times 10^5 \]

So, the total weight of the dump truck with the trash added is \( 2.953 \times 10^5 \) pounds.

Thus, the answer in scientific notation is:

2.953×10^5 pounds.