(9x10%5E6)-in-scientific-notation.jpeg "(7.68x10^2)(9x10^6) In Scientific Notation")
Multiplying Numbers in Scientific Notation: (7.68 x 10²) (9 x 10⁶)
This article will guide you through multiplying numbers expressed in scientific notation, specifically the expression (7.68 x 10²) (9 x 10⁶).
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 (positive or negative)
Multiplying Numbers in Scientific Notation
To multiply numbers in scientific notation, we follow these steps:
- Multiply the coefficients (a values): 7.68 x 9 = 69.12
- Add the exponents (b values): 2 + 6 = 8
- Combine the results: 69.12 x 10⁸
Adjusting to Proper Scientific Notation
The result we got (69.12 x 10⁸) is not in proper scientific notation because the coefficient is greater than 10. To correct this, we move the decimal point one place to the left and increase the exponent by one:
69.12 x 10⁸ = 6.912 x 10⁹
Final Answer
Therefore, the product of (7.68 x 10²) (9 x 10⁶) expressed in proper scientific notation is 6.912 x 10⁹.