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). The simplest fraction represents the exact value of the decimal using the smallest possible integers for numerator and denominator.

2. How Does the Calculator Work?

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

Algorithm: The calculator iteratively approximates the decimal value with increasingly accurate fractions until it finds the simplest exact representation.

3. Importance of Fraction Conversion

Details: Converting decimals to fractions is important in many mathematical and scientific applications where exact ratios are preferred over decimal approximations.

4. Using the Calculator

Tips: Enter any decimal value between 0 and 1. The calculator will return the simplest fraction that exactly represents that decimal value.

5. Frequently Asked Questions (FAQ)

Q1: Why is 0.253623188 equal to 35/138?
A: Because 35 divided by 138 equals exactly 0.253623188 when calculated to 9 decimal places.

Q2: What if my decimal doesn't convert to a simple fraction?
A: Some decimals (like irrational numbers) cannot be exactly represented as fractions, but the calculator will find the closest approximation within tolerance.

Q3: How accurate is the conversion?
A: The conversion is mathematically exact for terminating decimals and very precise for repeating decimals.

Q4: Can I convert values greater than 1?
A: This calculator is designed for values between 0 and 1. For values >1, subtract the integer part and convert the decimal part separately.

Q5: What's the maximum denominator the calculator will use?
A: The calculator will find the simplest fraction, so denominators are kept as small as possible while maintaining accuracy.