-x-(9-x-10%5E7)-in-standard-form.jpeg "(5 X 10^3) X (9 X 10^7) In Standard Form")
Scientific Notation: Simplifying (5 x 10^3) x (9 x 10^7) in Standard Form
In this article, we will explore how to simplify the expression (5 x 10^3) x (9 x 10^7) and represent it in standard form.
Understanding Scientific Notation
In scientific notation, a number is represented as a product of a number between 1 and 10, and a power of 10. For example, the number 4500 can be written in scientific notation as 4.5 x 10^3.
Simplifying the Expression
To simplify the expression (5 x 10^3) x (9 x 10^7), we need to follow the order of operations (PEMDAS):
- Multiply the coefficients:
5 x 9 = 45 - Multiply the powers of 10:
10^3 x 10^7 = 10^(3+7) = 10^10
So, the simplified expression is 45 x 10^10.
Standard Form
In standard form, the coefficient must be between 1 and 10. Since our coefficient is 45, which is greater than 10, we need to divide it by 10 and multiply the power of 10 by 1:
45 x 10^10 = 4.5 x 10^(10+1) = 4.5 x 10^11
Therefore, the standard form of the expression (5 x 10^3) x (9 x 10^7) is 4.5 x 10^11.
