1. What is Decimal to Fraction Conversion?

Decimal to fraction conversion is the process of expressing a decimal number as a fraction (a ratio of two integers). The reduced form means the numerator and denominator have no common divisors other than 1.

2. How Does the Calculator Work?

The calculator uses continued fractions to find the best rational approximation:

Where:

• \( a \) — Numerator (integer)
• \( b \) — Denominator (integer)
• gcd — Greatest common divisor

Explanation: The algorithm finds the simplest fraction that approximates the decimal within a small tolerance.

3. Importance of Reduced Fractions

Details: Reduced fractions provide the simplest exact representation of decimal numbers, which is important for precise calculations and avoiding rounding errors.

4. Using the Calculator

Tips: Enter any decimal number (positive or negative). The calculator will return the simplest fraction representation or the exact integer if applicable.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the conversion?
A: The conversion is accurate to within 6 decimal places by default, providing the simplest fraction within that tolerance.

Q2: What about repeating decimals?
A: The calculator can handle repeating decimals by finding their exact fractional representation.

Q3: Why is my result showing a large denominator?
A: Some decimals require larger denominators for precise representation. The calculator always returns the simplest form.

Q4: Can it convert fractions back to decimals?
A: This calculator only converts decimals to fractions. For reverse conversion, divide numerator by denominator.

Q5: What's the maximum decimal input?
A: There's no strict maximum, but extremely large or small numbers may lose precision due to floating-point limitations.