Evaluate (pi*5^2)/2
The problem presents an arithmetic expression that needs to be evaluated. It involves the mathematical constant pi (approximately 3.14159), the exponentiation of the number 5 to the power of 2, and the division of the resulting product by 2. The task is to perform the calculations according to the order of operations: squaring the number 5, multiplying that result by pi, and finally dividing the product of these operations by 2.
$\frac{\pi \cdot 5^{2}}{2}$
Answer
Solution:
Step 1:
Compute the square of $5$, which gives $5^2 = 25$. The expression becomes $\frac{\pi \cdot 25}{2}$.
Step 2:
Rearrange the terms to place the constant before $\pi$. The expression now reads $\frac{25\pi}{2}$.
Step 3:
Present the final result in its various representations:
- Exact Form: $\frac{25\pi}{2}$
- Decimal Form: Approximately $39.26990816 \ldots$
Knowledge Notes:
The problem involves evaluating a mathematical expression that includes the constant $\pi$ (pi), exponentiation, and division. Here are the relevant knowledge points:
Exponentiation: This is the operation of raising one number (the base) to the power of another (the exponent). In this case, $5^2$ means $5$ multiplied by itself, which equals $25$.
Multiplication with $\pi$: $\pi$ is an irrational number approximately equal to $3.14159$. It is often used in formulas related to circles and spheres. In this problem, $\pi$ is being multiplied by $25$.
Division: The division operation is represented by the symbol $/$. Here, the product of $25$ and $\pi$ is being divided by $2$.
Order of Operations: In mathematics, the order of operations dictates the sequence in which a complex expression should be evaluated. According to this convention, exponentiation is performed before multiplication and division.
Representation of Numbers: The final result of a mathematical expression can be represented in different forms. The exact form maintains the mathematical symbols and constants, while the decimal form converts the expression into a decimal number, which may be an approximation if it involves irrational numbers like $\pi$.
Use of LaTeX in Formatting: LaTeX is a typesetting system that is widely used for the communication and publication of scientific documents. It is used here to format mathematical expressions and symbols for clarity and precision.
