1. What is Decimal to Fraction Conversion?

Decimal to fraction conversion is the process of converting a decimal number to its equivalent fractional representation. This is useful in many mathematical and real-world applications where fractions are preferred over decimals.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( d \) — Decimal number (unitless)
• \( a \) — Numerator (unitless)
• \( b \) — Denominator (unitless)

Explanation: The calculator uses a continued fraction algorithm to find the simplest fraction that represents the decimal value within a specified tolerance.

3. Importance of Fraction Conversion

Details: Fractions are often more intuitive than decimals, especially in measurements, ratios, and proportions. Many fields like carpentry, cooking, and engineering prefer fractional measurements.

4. Using the Calculator

Tips: Enter any decimal number (positive or negative) and the calculator will return the simplest fraction representation. For repeating decimals, enter as many decimal places as possible for better accuracy.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum decimal precision supported?
A: The calculator supports up to 15 significant digits, which is the precision limit of PHP floating-point numbers.

Q2: How does the calculator handle repeating decimals?
A: The algorithm finds the simplest fraction within a tolerance of 1×10⁻⁶, which works well for most repeating decimals.

Q3: Can I convert negative decimals?
A: Yes, the calculator handles negative decimals and returns fractions with negative numerators.

Q4: Why might the fraction not match exactly?
A: Some decimals can't be represented exactly as fractions with limited-digit denominators. The calculator finds the closest approximation.

Q5: What about very large denominators?
A: The algorithm limits denominators to reasonable sizes for practical use, though extremely precise conversions may require larger denominators.