1. What is Recurring Decimal to Fraction Conversion?

Recurring (repeating) decimals are decimal numbers that have digits repeating infinitely. This calculator converts such decimals to their exact fractional equivalents, providing precise mathematical representations.

2. How Does the Calculator Work?

The calculator uses the following mathematical approach:

Example: For 0.1212...

• Non-repeating part: "" (empty)
• Repeating part: "12"
• Numerator: 12 - 0 = 12
• Denominator: 100 - 1 = 99
• Fraction: 12/99 = 4/33 (simplified)

3. Importance of Decimal-Fraction Conversion

Details: Converting recurring decimals to fractions is essential for exact mathematical representations, avoiding rounding errors in calculations, and understanding number theory concepts.

4. Using the Calculator

Tips: Enter the recurring decimal in either format: 0.333... or 0.(3) for 1/3, or 0.123123... or 0.(123) for 41/333. The calculator will return the simplified fraction.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between terminating and recurring decimals?
A: Terminating decimals have finite digits (e.g., 0.5), while recurring decimals have infinite repeating patterns (e.g., 0.333...).

Q2: Can all recurring decimals be converted to fractions?
A: Yes, all recurring decimals represent rational numbers and can be expressed as fractions of integers.

Q3: How to input mixed recurring decimals?
A: For decimals like 0.1666... (1/6), input as 0.1(6) or 0.1666... - the calculator will handle both.

Q4: What about non-repeating infinite decimals?
A: Non-repeating infinite decimals (like π) are irrational and cannot be expressed as fractions of integers.

Q5: Why does the fraction sometimes simplify to a whole number?
A: Some decimals like 0.999... exactly equal 1, as 9/9 = 1 when simplified.