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Simplifying Scientific Notation: (3 x 10²) x (2 x 10⁻⁴)
This article will guide you through the process of simplifying the multiplication of two numbers expressed in scientific notation: (3 x 10²) x (2 x 10⁻⁴).
Understanding Scientific Notation
Scientific notation is a way of representing very large or very small numbers in a compact and manageable form. It consists of two parts:
- A coefficient: A number between 1 and 10.
- A base 10 raised to a power (exponent): This indicates how many places the decimal point is shifted.
Multiplication of Numbers in Scientific Notation
To multiply numbers in scientific notation, follow these steps:
- Multiply the coefficients: 3 x 2 = 6
- Add the exponents: 2 + (-4) = -2
Therefore, the simplified result is 6 x 10⁻².
Explanation
Let's break down why we add the exponents:
- 10² represents 100 (10 x 10).
- 10⁻⁴ represents 0.0001 (1 / 10⁴).
Multiplying these together, we have:
(3 x 10²) x (2 x 10⁻⁴) = (3 x 2) x (10² x 10⁻⁴) = 6 x 10⁻²
This demonstrates that multiplying powers of 10 with different exponents is equivalent to adding their exponents.
Conclusion
The simplified form of (3 x 10²) x (2 x 10⁻⁴) is 6 x 10⁻². Understanding scientific notation and the rules for multiplying numbers in this form is crucial in various scientific and mathematical calculations.