In Scientific Notation, \[$670,000,000 + 700,000,000 = ?\$\]A) \[$1.37 \times 10^{-9}\$\] B) \[$1.37 \times 10^7\$\] C) \[$1.37 \times 10^8\$\] D) \[$1.37 \times 10^9\$\]
What is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. This notation is commonly used in mathematics, physics, and engineering to simplify complex calculations and make them easier to understand.
How to Write Numbers in Scientific Notation
To write a number in scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10. The power of 10 is determined by the number of places you need to move the decimal point to get a number between 1 and 10.
For example, let's consider the number 670,000,000. To write this number in scientific notation, you need to move the decimal point 8 places to the left to get 6.7. Since you moved the decimal point 8 places to the left, the power of 10 is 10^8.
Therefore, the scientific notation of 670,000,000 is 6.7 x 10^8.
Adding Numbers in Scientific Notation
Now that we have a good understanding of scientific notation, let's move on to adding numbers in scientific notation. When adding numbers in scientific notation, you need to make sure that the powers of 10 are the same. If the powers of 10 are different, you need to adjust the numbers so that the powers of 10 are the same.
Let's consider the example given in the problem: 670,000,000 + 700,000,000. To add these numbers, we need to express them in scientific notation.
The scientific notation of 670,000,000 is 6.7 x 10^8.
The scientific notation of 700,000,000 is 7 x 10^8.
Since the powers of 10 are the same, we can add the numbers directly.
6.7 x 10^8 + 7 x 10^8 = 13.7 x 10^8
Simplifying the Answer
Now that we have added the numbers, we need to simplify the answer. To simplify the answer, we need to express it in a more manageable form.
The answer 13.7 x 10^8 can be simplified by expressing it as a number between 1 and 10 and a power of 10.
To do this, we need to move the decimal point 8 places to the left to get 1.37. Since we moved the decimal point 8 places to the left, the power of 10 is 10^8.
Therefore, the simplified answer is 1.37 x 10^8.
Conclusion
In conclusion, scientific notation is a powerful tool for simplifying complex numbers. By expressing numbers in scientific notation, we can make calculations easier and more manageable. When adding numbers in scientific notation, we need to make sure that the powers of 10 are the same. If the powers of 10 are different, we need to adjust the numbers so that the powers of 10 are the same. By following these steps, we can simplify complex calculations and make them easier to understand.
Answer
The correct answer is C) 1.37 x 10^8.
Why is this the correct answer?
This is the correct answer because we added the numbers 670,000,000 and 700,000,000 and simplified the answer to 1.37 x 10^8.
What are the other options?
The other options are:
A) 1.37 x 10^-9
B) 1.37 x 10^7
D) 1.37 x 10^9
These options are incorrect because they do not accurately represent the result of adding 670,000,000 and 700,000,000.
Why are these options incorrect?
These options are incorrect because they do not accurately represent the result of adding 670,000,000 and 700,000,000. The correct answer is 1.37 x 10^8, which is option C.
What is the significance of this problem?
This problem is significant because it demonstrates the importance of scientific notation in simplifying complex calculations. By expressing numbers in scientific notation, we can make calculations easier and more manageable. This problem also demonstrates the importance of following the correct steps when adding numbers in scientific notation.
What are the implications of this problem?
The implications of this problem are that it demonstrates the importance of scientific notation in simplifying complex calculations. By expressing numbers in scientific notation, we can make calculations easier and more manageable. This problem also demonstrates the importance of following the correct steps when adding numbers in scientific notation.
What are the limitations of this problem?
The limitations of this problem are that it only deals with adding numbers in scientific notation. It does not cover other operations such as subtraction, multiplication, and division.
What are the future directions of this problem?
The future directions of this problem are to explore other operations such as subtraction, multiplication, and division in scientific notation. It would also be interesting to explore the application of scientific notation in real-world problems.
References
- [1] "Scientific Notation" by Math Open Reference
- [2] "Scientific Notation" by Khan Academy
- [3] "Scientific Notation" by Wolfram MathWorld
Conclusion
In conclusion, scientific notation is a powerful tool for simplifying complex numbers. By expressing numbers in scientific notation, we can make calculations easier and more manageable. When adding numbers in scientific notation, we need to make sure that the powers of 10 are the same. If the powers of 10 are different, we need to adjust the numbers so that the powers of 10 are the same. By following these steps, we can simplify complex calculations and make them easier to understand.
Answer
The correct answer is C) 1.37 x 10^8.