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). This is particularly useful in mathematics, engineering, and various practical applications where exact ratios are preferred over decimal approximations.

2. How Does the Calculator Work?

The calculator uses the following equation:

Where:

• \( d \) — Decimal value (input)
• \( a \) — Numerator (integer part of the fraction)
• \( b \) — Denominator (integer part of the fraction)

Explanation: The calculator uses a continued fraction algorithm to find the best rational approximation to the given decimal value within a specified tolerance.

3. Importance of Fraction Conversion

Details: Fractions often provide more precise representations than decimals, especially for repeating decimals. They're essential in many mathematical operations, measurements, and ratio calculations.

4. Using the Calculator

Tips: Enter any positive decimal value. The calculator will return the simplest fraction that approximates your decimal value. For repeating decimals, the fraction will be exact.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is the conversion?
A: The calculator provides the most accurate fraction representation within a tolerance of 1.0E-6.

Q2: What about negative decimals?
A: This calculator handles positive values only. For negative values, convert the absolute value and add the negative sign to the numerator.

Q3: Why does 0.333... return 1/3?
A: The calculator recognizes common repeating decimals and returns their exact fractional equivalents.

Q4: What's the maximum denominator allowed?
A: There's no strict maximum, but very precise decimals may result in large denominators.

Q5: Can I convert fractions back to decimals?
A: Yes, simply divide the numerator by the denominator.