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.
To find the weight of the dump truck when 15,300 pounds of trash is added, we need to add the two weights together.
2.8×105 pounds + 15,300 pounds
Let's first write the weight of the dump truck in scientific notation:
2.8×105 pounds = 2.8 × 10^5 pounds
Now we can add the weights:
2.8×105 pounds + 15,300 pounds = 2.8 × 10^5 pounds + 1.53 × 10^4 pounds
To combine the terms, we need them to have the same exponent in the power of 10. Thus, let's convert 1.53 × 10^4 pounds into scientific notation:
1.53 × 10^4 pounds = 1.53 × 10^4 × 10^1 pounds = 1.53 × 10^5 pounds
Now we can add:
2.8 × 10^5 pounds + 1.53 × 10^5 pounds = 4.33 × 10^5 pounds
Therefore, the weight of the dump truck when 15,300 pounds of trash is added is approximately 4.33 × 10^5 pounds in scientific notation.
To find the weight of the dump truck with 15,300 pounds of trash added, we need to add the weight of the trash to the empty weight of the truck.
Empty weight of the truck: 2.8×10^5 pounds
Weight of trash added: 15,300 pounds
To add these weights, we can simply add the values:
2.8×10^5 pounds + 15,300 pounds = 2.8×10^5 + 1.53×10^4 pounds
Now, let's simplify the expression:
2.8×10^5 + 1.53×10^4 = 2.8×10^5 + (1.53×10^4 × 10^1) = 2.8×10^5 + 1.53×10^5 = (2.8 + 1.53) × 10^5
Adding the coefficients:
2.8 + 1.53 = 4.33
Final weight in scientific notation:
4.33 × 10^5 pounds
To determine the weight of the dump truck after adding the trash, you can simply add the weight of the empty truck to the weight of the trash.
Given that the empty dump truck weighs 2.8×10^5 pounds and adding 15,300 pounds of trash, you can express the weight of the truck after adding the trash as:
2.8×10^5 pounds + 15,300 pounds = 2.8×10^5 + 1.53×10^4 pounds
Now, to add these values, you need to ensure that you have the same exponent (power of 10). To do this, convert 1.53×10^4 to the same form as 2.8×10^5.
1.53×10^4 pounds = 0.153×10^5 pounds
Now, you can add the weights:
2.8×10^5 pounds + 0.153×10^5 pounds = 2.953×10^5 pounds
Therefore, the weight of the dump truck after adding 15,300 pounds of trash is 2.953×10^5 pounds.