Add Numbers in Scientific Notation Quick Check

Question

3 of 53 of 5 Items
Question
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

2.953×105
pounds
2.953 times 10 superscript 5 baseline pounds

15,302.8 pounds
15,302.8 pounds

4.33×105
pounds
4.33 times 10 superscript 5 baseline pounds

29,530 pounds
29,530 pounds
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Answer 1

To add the weights correctly in scientific notation, we first need to convert 15,300 pounds into scientific notation.

15,300 can be written as: \[ 1.53 \times 10^4 \]

Now we can add this to the weight of the empty dump truck, which is: \[ 2.8 \times 10^5 \]

Before we can add these two values, we need them to have the same exponent. The term \( 1.53 \times 10^4 \) can be converted to have the same exponent as \( 2.8 \times 10^5 \):

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

Now we can add:

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

So, the weight of the dump truck after adding the trash is \( 2.953 \times 10^5 \) pounds.

Correct Response: 2.953×10^5 pounds