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Multiplying Numbers in Scientific Notation: (2 x 10^-3)(3 x 10^-6)
This article will explain how to multiply numbers expressed in scientific notation, specifically focusing on the example (2 x 10^-3)(3 x 10^-6).
Understanding Scientific Notation
Scientific notation is a convenient way to express very large or very small numbers. It follows the format: a x 10^b, where:
- a is a number between 1 and 10 (the coefficient)
- b is an integer (the exponent)
Multiplying Numbers in Scientific Notation
To multiply two numbers in scientific notation, follow these steps:
- Multiply the coefficients: (2 x 3) = 6
- Add the exponents: (-3) + (-6) = -9
Therefore, (2 x 10^-3)(3 x 10^-6) = 6 x 10^-9.
Example Explanation
In our example:
- 2 and 3 are the coefficients.
- -3 and -6 are the exponents.
By multiplying the coefficients and adding the exponents, we obtain the final result of 6 x 10^-9.
Conclusion
Multiplying numbers in scientific notation is a straightforward process. By understanding the rules of exponents and coefficient multiplication, you can easily compute the product of two numbers in scientific notation.