1. What is 0.7853981634?

0.7853981634 is a decimal approximation of π/4 (pi divided by 4). This value appears frequently in mathematics, particularly in trigonometry and geometry calculations involving angles of 45 degrees or circular sectors.

2. How Does the Conversion Work?

The calculator recognizes special constants like π/4 and converts them to their exact fractional form:

For general decimals, the calculator:

• Multiplies by a large power of 10 to make an integer numerator
• Uses 10^n as the denominator
• Simplifies the fraction using greatest common divisor (GCD)

3. Mathematical Significance

Details: π/4 represents the ratio of the area of a quarter-circle to the area of its circumscribed square. It's also equal to 45 degrees in radians.

4. Using the Calculator

Tips: Enter any decimal value to see its fractional approximation. The calculator automatically detects special constants like π/4.

5. Frequently Asked Questions (FAQ)

Q1: Why is π/4 important?
A: π/4 appears in many formulas including area of a circle sector, trigonometric identities, and polar coordinates.

Q2: How accurate is this conversion?
A: For π/4, it's exact. For other decimals, accuracy depends on the tolerance setting.

Q3: Can I convert other special constants?
A: Yes, the calculator recognizes common constants like π, e, and their rational multiples.

Q4: What's the maximum decimal precision?
A: The calculator handles up to 10 decimal places accurately.

Q5: Why would I need this conversion?
A: Fractional forms are often more meaningful in mathematical proofs and geometric interpretations.