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 particularly useful in mathematics, engineering, and everyday measurements where fractional representations are preferred.

2. How Does the Calculator Work?

The calculator uses continued fractions to find the best rational approximation:

Where:

• \( d \) — Input decimal value
• \( a \) — Numerator of the resulting fraction
• \( b \) — Denominator of the resulting fraction

Explanation: The algorithm finds the closest fraction representation within the specified precision tolerance.

3. Importance of Fraction Conversion

Details: Fractions are often more intuitive than decimals for measurements (like 1/2" instead of 0.5"), and are essential in many mathematical operations and real-world applications.

4. Using the Calculator

Tips: Enter any decimal value and select your desired precision level. Higher precision will yield more accurate but potentially more complex fractions.

5. Frequently Asked Questions (FAQ)

Q1: Why doesn't my decimal convert exactly?
A: Some decimals (like 0.333...) are irrational and can only be approximated. The calculator finds the closest fraction within your precision setting.

Q2: What's the maximum decimal I can convert?
A: The calculator works with any reasonable decimal input, but extremely large or small values may lose precision.

Q3: How do I choose the right precision?
A: For most everyday uses, medium precision (1/1000) is sufficient. Use high precision for technical applications.

Q4: Why do some fractions simplify?
A: The calculator automatically reduces fractions to their simplest form (e.g., 2/4 becomes 1/2).

Q5: Can I convert repeating decimals?
A: Yes, but you'll need to select a precision that captures enough of the repeating pattern for a good approximation.