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Answer :
To solve the problem of adding [tex]\(670,000,000\)[/tex] and [tex]\(700,000,000\)[/tex] and expressing the sum in scientific notation, let's break it down step-by-step:
1. Add the two numbers:
[tex]\[
670,000,000 + 700,000,000 = 1,370,000,000
\][/tex]
2. Convert the result into scientific notation:
- In scientific notation, a number is written as [tex]\(a \times 10^n\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(n\)[/tex] is an integer.
- For [tex]\(1,370,000,000\)[/tex], find a way to write it in the form of [tex]\( a \times 10^n \)[/tex].
3. Adjust the number to fit the scientific notation requirements:
- Move the decimal point in [tex]\(1,370,000,000\)[/tex] so that there is only one non-zero digit to its left. This gives us 1.37.
- To convert [tex]\(1,370,000,000\)[/tex] into [tex]\(1.37\)[/tex], you move the decimal point 9 places to the left.
4. Determine the exponent:
- The value of the exponent [tex]\(n\)[/tex] is equal to the number of places the decimal point has been moved. In this case, it is moved 9 places.
- So, the scientific notation is [tex]\(1.37 \times 10^9\)[/tex].
Thus, the final answer is [tex]\(1.37 \times 10^9\)[/tex].
1. Add the two numbers:
[tex]\[
670,000,000 + 700,000,000 = 1,370,000,000
\][/tex]
2. Convert the result into scientific notation:
- In scientific notation, a number is written as [tex]\(a \times 10^n\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(n\)[/tex] is an integer.
- For [tex]\(1,370,000,000\)[/tex], find a way to write it in the form of [tex]\( a \times 10^n \)[/tex].
3. Adjust the number to fit the scientific notation requirements:
- Move the decimal point in [tex]\(1,370,000,000\)[/tex] so that there is only one non-zero digit to its left. This gives us 1.37.
- To convert [tex]\(1,370,000,000\)[/tex] into [tex]\(1.37\)[/tex], you move the decimal point 9 places to the left.
4. Determine the exponent:
- The value of the exponent [tex]\(n\)[/tex] is equal to the number of places the decimal point has been moved. In this case, it is moved 9 places.
- So, the scientific notation is [tex]\(1.37 \times 10^9\)[/tex].
Thus, the final answer is [tex]\(1.37 \times 10^9\)[/tex].
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