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 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 certain calculations. They can provide exact values where decimals might be repeating approximations.

4. Using the Calculator

Tips: Enter any positive decimal number. The calculator will return the simplest fraction representation. For exact fractions, enter decimals that can be precisely represented as fractions (like 0.5, 0.25, etc.).

5. Frequently Asked Questions (FAQ)

Q1: Why does my decimal give a complex fraction?
A: Some decimals (like 0.333...) are repeating and require fractions to be accurately represented. The calculator finds the simplest fraction within a small tolerance.

Q2: What's the maximum decimal value I can enter?
A: There's no strict maximum, but very large decimals may result in very large fractions that are hard to interpret.

Q3: Why does 0.33 give 33/100 but 0.333 gives 1/3?
A: The calculator recognizes common fractional patterns. 0.333 is close enough to 1/3 (0.333...) to return that simplified fraction.

Q4: Can I enter negative decimals?
A: This calculator only handles positive decimals. For negative numbers, convert the absolute value and add the negative sign to the numerator.

Q5: How accurate is the conversion?
A: The conversion is accurate to within 0.0001% by default. You can adjust the tolerance in the code for more precise conversions.