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Simplifying Scientific Notation: (3 x 10^2)(4 x 10^3)
This article will demonstrate how to simplify the multiplication of two numbers expressed in scientific notation: (3 x 10^2)(4 x 10^3).
Understanding Scientific Notation
Scientific notation is a way to express very large or very small numbers in a compact and convenient form. It follows the format: a x 10^b, where:
- a is a number between 1 and 10 (but not including 10).
- b is an integer representing the power of 10.
Simplifying the Expression
To simplify the expression (3 x 10^2)(4 x 10^3), we can follow these steps:
- Multiply the coefficients: 3 x 4 = 12
- Multiply the powers of 10: 10^2 x 10^3 = 10^(2+3) = 10^5
Therefore, the simplified expression is 12 x 10^5.
Converting to Standard Form
While the simplified form is correct, it's not always in standard scientific notation. To express the answer in standard scientific notation, we need to adjust the coefficient:
- Move the decimal point one place to the left: 12 x 10^5 becomes 1.2 x 10^6
Final Answer: The simplified expression (3 x 10^2)(4 x 10^3) in standard scientific notation is 1.2 x 10^6.
Key Takeaways
- Multiplying numbers in scientific notation involves multiplying the coefficients and adding the exponents of the powers of 10.
- Ensure the final answer is in standard scientific notation, with the coefficient between 1 and 10 (but not including 10).