1. What is Pi (π)?

Definition: Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter.

Importance: It appears in many formulas across mathematics and physics, particularly those involving circles or periodic phenomena.

2. Common Pi Approximations

The calculator provides two common approximations:

22/7 Fraction: This simple fraction gives π ≈ 3.142857 (accurate to 2 decimal places)

Decimal Approximation: 3.14159 is accurate to 5 decimal places

3. Mathematical Properties of Pi

Details: Pi is an irrational number (cannot be expressed as a simple fraction) and a transcendental number (not a root of any non-zero polynomial equation with rational coefficients).

4. Using the Calculator

Tips: Select your preferred approximation method (22/7 fraction or 5-decimal approximation) and click Calculate.

5. Frequently Asked Questions (FAQ)

Q1: Why use approximations instead of the exact value?
A: Since π is irrational, we must use approximations for practical calculations. The exact value has infinite non-repeating digits.

Q2: Which approximation is more accurate?
A: The decimal approximation (3.14159) is more precise than 22/7 (3.142857).

Q3: When should I use 22/7 instead of decimal?
A: Use 22/7 when working with fractions or when a rough estimate is sufficient. Use decimal for more precise calculations.

Q4: How many digits of pi are known?
A: As of 2023, pi has been calculated to over 100 trillion digits, though most applications need only a few dozen.

Q5: What's the exact value of pi?
A: Pi has no exact finite representation - it's an infinite non-repeating decimal. The sequence begins 3.141592653589793...