An empty dump truck weighs about 2.8 x 10^5 pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific Notation.
a 4.33 x 10^5 pounds
b 2.953 x 10^5 pounds
c 15,302.8 pounds
d 29,530 pounds
To find the total weight, we need to add the weight of the empty truck and the weight of the trash added.
Weight of the empty truck = 2.8 x 10^5 pounds
Weight of the trash added = 15,300 pounds
Total weight = Weight of the empty truck + Weight of the trash added
= 2.8 x 10^5 pounds + 15,300 pounds
Adding these two weights, we get:
Total weight = 2.8 x 10^5 pounds + 15,300 pounds
= 2.8 x 10^5 + 15,300
= 2.8 x 10^5 + 1.53 x 10^4
= 2.953 x 10^5 pounds
Therefore, the answer is b) 2.953 x 10^5 pounds.
To find the total weight of the dump truck with the added trash, we need to add the weight of the empty truck to the weight of the trash:
Empty truck weight: 2.8 x 10^5 pounds
Trash weight: 15,300 pounds
Adding these two weights together:
2.8 x 10^5 pounds + 15,300 pounds = 2.8 x 10^5 + 1.53 x 10^4 pounds
To convert this to scientific notation, we need to adjust the decimal point so that there is only one non-zero digit before it. In this case, we have 2.8 x 10^5 and 1.53 x 10^4.
Combining these two terms:
2.8 x 10^5 + 1.53 x 10^4 pounds = 2.8 x 10^5 + 0.153 x 10^5 pounds
Adding the numbers together:
2.8 x 10^5 + 0.153 x 10^5 = 2.953 x 10^5 pounds
So the correct answer is option b: 2.953 x 10^5 pounds.
To find the weight of the dump truck with the added trash, you need to add the weight of the trash to the weight of the empty dump truck.
Given:
Weight of empty dump truck = 2.8 x 10^5 pounds
Weight of trash added = 15,300 pounds
To find the total weight, you perform the addition: 2.8 x 10^5 + 15,300.
To make the calculation, we need to convert 15,300 to scientific notation. It can be represented as 1.53 x 10^4.
So, the calculation becomes: 2.8 x 10^5 + 1.53 x 10^4.
When adding numbers in scientific notation, you can only add them if they have the same exponent. In this case, both numbers have different exponents: 10^5 and 10^4.
To add them, you need to make the exponents the same. You can do this by converting the number with the lower exponent (10^4) to have the same exponent as the other number (10^5).
To convert 10^4 to have the same exponent as 10^5, you multiply the number by 10. That becomes: 1.53 x 10^4 * 10.
Now the exponents are the same: 10^5.
Performing the addition: 2.8 x 10^5 + 1.53 x 10^4 * 10 = 2.8 x 10^5 + 1.53 x 10^5.
Finally, by adding the numbers: (2.8 + 1.53) x 10^5 = 4.33 x 10^5.
Therefore, the weight of the dump truck with the added trash is approximately 4.33 x 10^5 pounds.
So, the correct answer is (a) 4.33 x 10^5 pounds.