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Multiplying Numbers in Scientific Notation: A Step-by-Step Guide
This article will guide you through multiplying numbers expressed in scientific notation, using the example of (6 x 10^-8) x (4 x 10^-4).
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 (called the coefficient).
- b is an integer (called the exponent).
Multiplying Numbers in Scientific Notation
To multiply numbers in scientific notation, follow these steps:
- Multiply the coefficients: 6 x 4 = 24
- Add the exponents: -8 + (-4) = -12
Therefore, the product of (6 x 10^-8) and (4 x 10^-4) is 24 x 10^-12.
Expressing the Result in Standard Scientific Notation
The coefficient in the result (24) is not between 1 and 10. To express the result in standard scientific notation, we need to adjust the coefficient and exponent:
- Divide the coefficient by 10: 24 / 10 = 2.4
- Add 1 to the exponent: -12 + 1 = -11
Therefore, the final answer in standard scientific notation is 2.4 x 10^-11.
Conclusion
Multiplying numbers in scientific notation is a simple process involving multiplying the coefficients and adding the exponents. Remember to adjust the final result to ensure the coefficient is between 1 and 10. This method is widely used in various scientific fields, providing a compact and efficient way to work with extremely large or small numbers.