(3x10^8)+(2x10^7) In Standard Form

3 min read Jun 16, 2024
(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:

  1. 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)

  2. 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

  3. 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.

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