Add Numbers in Scientific Notation Quick Check
3 of 53 of 5 Items
Question
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
4.33×10^5 pounds
4.33 times 10 superscript 5 baseline pounds
29,530 pounds
29,530 pounds
2.953×10^5 pounds
2.953 times 10 superscript 5 baseline pounds
15,302.8 pounds
15,302.8 pounds
To find the weight of the dump truck with the added 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).
2.8×10^5 + 15,300 = 4.33×10^5 pounds
So, 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 is added (15,300 pounds).
First, let's write both numbers in scientific notation:
Empty dump truck weight = 2.8×10^5 pounds
Added trash weight = 1.53×10^4 pounds
To add these numbers, we need to have the same power of 10. Therefore, we need to convert the added trash weight to the same power of 10 as the empty dump truck weight.
To do this, we can move the decimal point in the added trash weight to the right until we have the same exponent as the empty dump truck weight. We will need to move it 1 place to the right.
Now, the added trash weight becomes:
Added trash weight = 1.53×10^4 pounds = 1.53×10^5 pounds
Next, we can add the two numbers:
2.8×10^5 pounds + 1.53×10^5 pounds = 4.33×10^5 pounds
So, the weight of the dump truck with the added trash is 4.33×10^5 pounds.
Therefore, the correct answer is: 4.33×10^5 pounds.
To find the weight of the dump truck after adding 15,300 pounds of trash, you will need to add the two numbers in scientific notation. Here's how you can do it step by step:
1. Start with the weight of the empty dump truck, which is given as 2.8×10^5 pounds in scientific notation.
This means that the weight is 2.8 multiplied by 10 raised to the power of 5.
2. Add the weight of the trash, which is given as 15,300 pounds.
Note that this number is not in scientific notation, so we need to convert it.
To convert 15,300 to scientific notation, you need to move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, the decimal point is already at the end, so there is only one non-zero digit to the left of it.
Therefore, 15,300 can be written as 1.53×10^4.
This means the weight is 1.53 multiplied by 10 raised to the power of 4.
3. Now, we can add the two numbers in scientific notation. Start by adding the coefficients (the numbers before the "×10^").
2.8 + 1.53 = 4.33
4. Next, we multiply the powers of 10.
10^5 × 10^4 = 10^(5+4) = 10^9
5. Finally, combine the coefficient from step 3 and the power of 10 from step 4 to get the final answer.
The weight of the dump truck after adding the trash is 4.33×10^9 pounds.
Therefore, the correct answer is 4.33×10^9 pounds.