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 mathematics, engineering, and other fields where exact fractional values are preferred over decimal approximations.

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 approximates the decimal value within a specified tolerance.

3. Importance of Fraction Conversion

Details: Fractional representations are often more precise than decimal approximations and are preferred in many mathematical and engineering applications where exact values are required.

4. Using the Calculator

Tips: Enter any decimal value (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: How accurate is the conversion?
A: The calculator uses a tolerance of 1×10⁻⁶, meaning the fraction will be accurate to at least 6 decimal places.

Q2: What about repeating decimals?
A: The algorithm can handle repeating decimals if enough decimal places are provided in the input.

Q3: Can it convert very large decimals?
A: Yes, but extremely large values may result in very large numerators and denominators.

Q4: How is the simplest fraction determined?
A: The calculator finds the fraction with the smallest denominator that satisfies the accuracy tolerance.

Q5: What if I enter 0?
A: The calculator will return 0/1 as the fraction representation.