Understanding Complex Mathematical Expressions and Their Evaluation

Multiplying, dividing, and evaluating complex mathematical expressions can often lead to confusion if the correct order of operations is not followed. In this article, we will break down the step-by-step process of evaluating a complex expression, specifically focusing on the expression 84.2 √4 1 2 1/48/2 1023 /2001623. This process is crucial for anyone dealing with mathematical expressions in various fields, including mathematics, engineering, and data science.

Breaking Down the Expression

The given expression is: 84.2 √4 1 2 1/48/2 1023 /2001623. To evaluate this, we need to follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 1: Simplify the Innermost Parentheses and Fractions

1/48/2 1023 – This is a fraction where the numerator is a complex expression. 1/48/2 1023 can be evaluated as: (1/48)*2*10^23 1/(48/2)*10^23 1/24*10^23. 84.2 √4 1 2 1/24*10^23 /2001623 – Now, we simplify further.

Step 2: Evaluate the Square Root and Exponents

√4 1 can be evaluated as follows:

√4 1 – Since the expression is √4 1, it should be interpreted as √(4*1) √4 2.

Squaring this result:

2^2 4.

Step 3: Apply Multiplication and Division

Multiplication and division are evaluated from left to right:

4 * 84.2 * 1/24 * 10^23 / 2001623.

First, simplify the multiplication and division:

84.2 * 4 336.8 336.8 * 1/24 14.033333333333334 14.033333333333334 * 10^23 / 2001623 ≈ 7.009009009009009 * 10^19 (rounded to four significant digits).

Step 4: Final Expression Evaluation

Combining the results from all the steps, we get:

Numerator: 7.009009009009009 * 10^19 Denominator: 2001623.

The final fraction is approximately:

N/D 7.009009009009009 * 10^19 / 2001623 ≈ 3.497 * 10^16.

Key Concepts and Keywords

Keywords: mathematical expression, complex operations, order of operations, PEMDAS, fraction evaluation, complex functions, scientific notation.

Keywords Summary: mathematical expression complex operations order of operations

Summary

Evaluating complex mathematical expressions requires a systematic approach by breaking them down into smaller, manageable parts. By following the order of operations, we can accurately evaluate complex expressions and derive the correct results. Understanding these principles is crucial in various fields, including engineering, data science, and more.