Question

An empty dump truck weighs about 2.8×10^5
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

29,530 pounds
29,530 pounds

4.33×10^5
4.33
×
10
5
pounds
4.33 times 10 superscript 5 baseline pounds

15,302.8 pounds
15,302.8 pounds

2.953×10^5
2.953
×
10
5
pounds

Answer 1

To find the total weight of the dump truck after adding 15,300 pounds of trash, we need to add the weight of the empty dump truck (2.8 × 10^5 pounds) to the weight of the trash (15,300 pounds).

First, we can convert 15,300 pounds into scientific notation.

15,300 = 1.53 × 10^4 pounds.

Now, we'll add the weights. To add them in scientific notation, we need them to have the same exponent:

We rewrite \(2.8 × 10^5\) as \(28 × 10^4\) (by multiplying 2.8 by 10, we move the decimal one place to the right and decrease the exponent by 1).

Now we can add:

\[
28 × 10^4 + 1.53 × 10^4 = (28 + 1.53) × 10^4 = 29.53 × 10^4
\]

Now, we convert \(29.53 × 10^4\) to standard scientific notation:

\[
29.53 × 10^4 = 2.953 × 10^5 \text{ (moving the decimal one place to the left increases the exponent by 1)}
\]

So the total weight of the dump truck with the trash added is:

\[
\text{Total weight} = 2.953 × 10^5 \text{ pounds.}
\]

Thus, the final answer is:

**2.953 × 10^5 pounds.**