The Correct Answer and Explanation is:
The correct answer is 1.37 x 10⁹.
Here is a detailed explanation of how to arrive at this answer.
The problem requires us to first calculate the sum of 670,000,000 and 700,000,000, and then to express that result in scientific notation.
Step 1: Perform the Addition
First, we add the two numbers together in their standard form.
670,000,000
- 700,000,000
= 1,370,000,000
The sum of the two numbers is one billion, three hundred seventy million.
Step 2: Convert the Sum to Scientific Notation
Scientific notation is a way to express numbers as a product of a coefficient and a power of 10. The format is a × 10^b, where the coefficient ‘a’ is a number greater than or equal to 1 but less than 10, and ‘b’ is an integer exponent.
- Find the coefficient (a): To find the coefficient, we take our sum, 1,370,000,000, and place a decimal point after the very first non-zero digit. The first digit is 1, so the coefficient becomes 1.37.
- Find the exponent (b): The exponent is determined by counting how many places we moved the decimal point. In the number 1,370,000,000, the decimal point is implicitly at the end. We moved it to the position between the 1 and the 3. Counting the places from right to left, we moved the decimal point 9 places. Since the original number is a large number (greater than 1), the exponent is positive. Therefore, the exponent is 9.
- Combine the parts: We combine the coefficient and the power of 10 to get the final answer.
This gives us 1.37 x 10⁹.
Alternative Method
Another valid method is to convert each number to scientific notation first. For this to work, the numbers must have the same exponent.
- 700,000,000 = 7.0 x 10⁸
- 670,000,000 = 6.7 x 10⁸
Now, add them: (6.7 x 10⁸) + (7.0 x 10⁸). Since the exponents are the same, we simply add the coefficients: 6.7 + 7.0 = 13.7. The result is 13.7 x 10⁸. This is not proper scientific notation because the coefficient 13.7 is not between 1 and 10. We must adjust it by moving the decimal one place to the left, making it 1.37. To balance this change, we increase the exponent by one, from 8 to 9. This again confirms the final answer is 1.37 x 10⁹.
