%2B(2x10%5E7)-in-standard-form.jpeg "(3x10^8)+(2x10^7) In Standard Form")
Adding Numbers in Scientific Notation: (3 x 10⁸) + (2 x 10⁷)
This article will guide you through the process of adding numbers in scientific notation, using the example of (3 x 10⁸) + (2 x 10⁷).
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers concisely. It follows the format:
a x 10^b
Where:
- a is a number between 1 and 10 (but not 10 itself)
- b is an integer representing the power of 10.
Adding Numbers in Scientific Notation
To add numbers in scientific notation, the powers of 10 must be the same. Here's how to proceed:
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Adjust the Exponents: If the exponents are different, adjust the smaller exponent to match the larger one.
In our example, we have (3 x 10⁸) + (2 x 10⁷). We need to make the exponent of the second term (2 x 10⁷) to be 8. We can do this by moving the decimal one place to the left and increasing the exponent by one:
(2 x 10⁷) = (0.2 x 10⁸)
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Add the Coefficients: Now that both numbers have the same exponent, we can add the coefficients:
(3 x 10⁸) + (0.2 x 10⁸) = (3 + 0.2) x 10⁸
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Simplify: Finally, perform the addition and express the result in standard scientific notation:
(3 + 0.2) x 10⁸ = 3.2 x 10⁸
Conclusion
Therefore, the sum of (3 x 10⁸) + (2 x 10⁷) in standard form is 3.2 x 10⁸. By following the steps outlined above, you can successfully add any two numbers in scientific notation.