1. What is the Decimal to Fraction Conversion?

The decimal to fraction conversion transforms a decimal number into an equivalent fraction (a ratio of two integers). 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 equation:

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 approximates the decimal value within a small 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 representations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: How does it handle repeating decimals?
A: The algorithm finds the closest fraction within a small tolerance (0.0001% by default).

Q3: What about irrational numbers?
A: Irrational numbers can only be approximated as fractions. The calculator will find the best simple fraction approximation.

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

Q5: What's the largest denominator it will return?
A: By default, denominators up to 1,000,000 are considered, but the algorithm prefers simpler fractions when possible.