Add Numbers in Scientific Notation Quick Check
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
29,530 pounds
29,530 pounds
15,302.8 pounds
15,302.8 pounds
4.33×105 pounds
4.33 times 10 superscript 5 baseline pounds
2.953×105 pounds
2.953 times 10 superscript 5 baseline pounds
The correct answer is 2.953 × 10^5 pounds.
To find the total weight of the dump truck after adding 15,300 pounds of trash, you can simply add the two values together.
First, let's convert 2.8 × 10^5 pounds to the correct scientific notation:
2.8 × 10^5 pounds
Next, we add 15,300 pounds to this value:
2.8 × 10^5 + 15,300 = 2.8 × 10^5 + 1.53 × 10^4
To add these values, we need to make sure they have the same exponent. Since 1.53 × 10^4 is equivalent to 1.53 × 10^5 (moving the decimal one place to the right), we can rewrite the equation as:
2.8 × 10^5 + 1.53 × 10^5 = 2.8 × 10^5 + 1.53 × 10^5 = 4.33 × 10^5 pounds
Therefore, the correct answer is 4.33 × 10^5 pounds.
To solve this problem, we need to add the weight of the empty dump truck (2.8×10^5 pounds) to the weight of the trash that was added (15,300 pounds).
1. First, let's convert the weight of the empty dump truck to scientific notation. The number 2.8×10^5 already represents it in scientific notation.
2. Next, we simply add the two values together.
2.8×10^5 pounds + 15,300 pounds = 2.8×10^5 pounds + 1.53×10^4 pounds
To add these numbers, we need to have the same exponent in the powers of 10. We can do this by converting 1.53×10^4 to scientific notation as well.
1.53×10^4 pounds can be written as 1.53×10^4×10^1 pounds, since 10^1 is equivalent to multiplying the number by 10.
Now, we can add the two numbers:
2.8×10^5 pounds + 1.53×10^4×10^1 pounds = 2.8×10^5 pounds + 1.53×10^4×10^1 pounds = 2.8×10^5 pounds + 1.53×10^5 pounds
3. Combine the coefficients:
2.8 + 1.53 = 4.33
4. The final answer is 4.33×10^5 pounds.