1. What is Repeating Decimal to Fraction Conversion?

This calculator converts repeating decimals into their exact fractional equivalents. Repeating decimals are numbers where one or more digits repeat infinitely after the decimal point.

2. How Does the Calculator Work?

The calculator uses the algebraic method:

Example for 0.333...:

1. Let x = 0.333...
2. Multiply by 10: 10x = 3.333...
3. Subtract original: 10x - x = 3.333... - 0.333...
4. 9x = 3 → x = 3/9 = 1/3

3. Importance of Fraction Conversion

Details: Fractions provide exact representations of numbers that are repeating decimals. This is important in precise mathematical calculations and theoretical work.

4. Using the Calculator

Tips: Enter the repeating decimal in either format: 0.333... or 0.(3). The calculator will return the simplest fractional form.

5. Frequently Asked Questions (FAQ)

Q1: What formats does the calculator accept?
A: It accepts both 0.abc... and 0.(abc) formats for repeating decimals.

Q2: How does it handle decimals with non-repeating and repeating parts?
A: For numbers like 0.12(345), it uses the full conversion method accounting for both parts.

Q3: What about terminating decimals?
A: Simple terminating decimals like 0.75 will be converted to fractions (3/4 in this case).

Q4: Are there limitations to this method?
A: The method works for all repeating decimals but requires correct input formatting.

Q5: How are fractions simplified?
A: The calculator uses the greatest common divisor (GCD) to reduce fractions to simplest form.