%2F(4x10%5E2)-in-standard-form.jpeg "(2x10^5)/(4x10^2) In Standard Form")
Simplifying the Expression: (2x10^5)/(4x10^2) in Standard Form
In this article, we will explore how to simplify the expression (2x10^5)/(4x10^2) and write it in standard form.
Understanding the Expression
The expression (2x10^5)/(4x10^2) is a complex fraction that involves numbers in scientific notation. To simplify this expression, we need to understand the rules of scientific notation and how to divide numbers in this form.
Rules of Scientific Notation
Scientific notation is a way of writing very large or very small numbers in a more compact form. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10. For example:
- 2 × 10^5 represents 200,000
- 4 × 10^2 represents 400
Simplifying the Expression
To simplify the expression (2x10^5)/(4x10^2), we can start by dividing the coefficients:
(2)/(4) = 0.5
Next, we need to divide the powers of 10. To do this, we subtract the exponent of the denominator from the exponent of the numerator:
10^(5-2) = 10^3
Now, we can combine the results:
0.5 × 10^3
Writing in Standard Form
To write the expression in standard form, we need to convert the coefficient to an integer. Since 0.5 is equal to 1/2, we can rewrite the expression as:
(1/2) × 10^3
This is the simplified expression in standard form.
Conclusion
In conclusion, we have successfully simplified the expression (2x10^5)/(4x10^2) and written it in standard form as (1/2) × 10^3. This process involved understanding the rules of scientific notation and applying them to simplify the expression. By following these steps, we can simplify complex fractions and write them in a more compact and readable form.
