x(4-x-10%5E7)-in-standard-form.jpeg "(6x10^8)x(4 X 10^7) In Standard Form")
Multiplying Numbers in Scientific Notation
In this article, we'll explore how to multiply numbers expressed in scientific notation, focusing on the specific example of (6 x 10⁸) x (4 x 10⁷).
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a compact and convenient form. It consists of two parts:
- A coefficient: This is a number between 1 and 10.
- A power of 10: This indicates the magnitude of the number.
For example, the number 600,000,000 can be written in scientific notation as 6 x 10⁸.
Multiplying Numbers in Scientific Notation
To multiply numbers in scientific notation, we follow these steps:
- Multiply the coefficients: Multiply the numbers in front of the powers of ten.
- Add the exponents of 10: Add the powers of ten.
Let's apply these steps to our example:
(6 x 10⁸) x (4 x 10⁷)
- Multiply the coefficients: 6 x 4 = 24
- Add the exponents: 8 + 7 = 15
Therefore, the product of (6 x 10⁸) and (4 x 10⁷) is 24 x 10¹⁵.
Standard Form
Although this answer is technically correct, it's not in standard scientific notation because the coefficient (24) is greater than 10. To convert it to standard scientific notation, we need to move the decimal point one place to the left and increase the exponent by one:
24 x 10¹⁵ = 2.4 x 10¹⁶
Therefore, the final answer in standard form is 2.4 x 10¹⁶.
Conclusion
Multiplying numbers in scientific notation involves multiplying the coefficients and adding the exponents. Remember to adjust the final answer to standard scientific notation if the coefficient is not between 1 and 10. This method simplifies calculations with large or small numbers, making them more manageable and easier to work with.