-x-(5-x-10%5E-8)-in-scientific-notation.jpeg "(7 X 10^-5) X (5 X 10^-8) In Scientific Notation")
Scientific Notation: A Simplified Approach to Complex Calculations
When dealing with extremely large or small numbers, scientific notation becomes an essential tool for simplifying calculations and making them more manageable. In this article, we will explore how to multiply two numbers in scientific notation, specifically (7 x 10^-5) and (5 x 10^-8).
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more compact and readable form. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10. The general format for scientific notation is:
a x 10^n
where 'a' is the coefficient and 'n' is the power of 10.
Multiplying Numbers in Scientific Notation
To multiply two numbers in scientific notation, we need to follow a simple rule:
( a x 10^n ) x ( b x 10^m ) = (a x b) x 10^(n+m)
Let's apply this rule to our example:
(7 x 10^-5) x (5 x 10^-8) = ?
First, we multiply the coefficients:
7 x 5 = 35
Next, we add the powers of 10:
-5 + (-8) = -13
So, our result in scientific notation is:
35 x 10^-13
Simplifying the Result
We can simplify our result by dividing the coefficient by 10 and increasing the power of 10 by 1:
35 x 10^-13 = 3.5 x 10^-12
And that's our final answer!
Conclusion
In conclusion, multiplying numbers in scientific notation is a straightforward process that simplifies complex calculations. By following the simple rule of multiplying coefficients and adding powers of 10, we can easily calculate the result of (7 x 10^-5) x (5 x 10^-8) in scientific notation, which is 3.5 x 10^-12.
