1. What is the Decimal to Fraction Formula?

The decimal to fraction formula represents a decimal number as a ratio of two integers (numerator and denominator). The formula is expressed as \( d = \frac{a}{b} \), where d is the decimal value, a is the numerator, and b is the denominator.

2. How Does the Calculator Work?

The calculator uses a continued fraction algorithm to find the simplest fraction representation:

Where:

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

Explanation: The algorithm finds the best rational approximation to the given decimal with a tolerance for precision.

3. Importance of Decimal to Fraction Conversion

Details: Converting decimals to fractions is important in mathematics, engineering, and everyday measurements where exact ratios are preferred over decimal approximations.

4. Using the Calculator

Tips: Enter any decimal value (positive or negative). The calculator will return the simplest fraction representation, along with the numerator and denominator separately.

5. Frequently Asked Questions (FAQ)

Q1: Why convert decimals to fractions?
A: Fractions often provide exact representations where decimals might be repeating or approximate. Many applications prefer fraction notation.

Q2: How accurate is the conversion?
A: The calculator uses a tolerance of 1.e-6 for precision. For most practical purposes, this provides exact or very close approximations.

Q3: What about repeating decimals?
A: The algorithm can handle repeating decimals by finding their exact fractional representation.

Q4: Are there limitations to this conversion?
A: Extremely large or small decimals may result in very large numerators/denominators. The calculator simplifies these where possible.

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