Repeating Decimal to Fraction Converter
Easily convert repeating decimals to fractions with our online converter. Understand the conversion process and get accurate results for any repeating decimal.
Use formats like 0.5, 0.333..., 0.(3), 1.2(45).
Fraction Visualization
Visual representation of the fraction .
Understanding Repeating Decimals
A repeating decimal, also known as a recurring decimal, is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero. For example, 1/3 = 0.333... which can be written as 0.(3).
To convert a repeating decimal to a fraction, we use algebraic methods. For a simple repeating decimal like 0.(3), let x = 0.333.... Then 10x = 3.333.... Subtracting x from 10x gives 9x = 3, so x = 3/9 = 1/3. For more complex decimals like 1.2(34), we adjust the multiplication factor and subtraction accordingly to eliminate the repeating part and solve for x as a fraction.
This tool uses an efficient algorithm based on continued fractions to find the exact fractional representation of any repeating decimal you input. You can use this converter to easily verify your manual calculations or quickly get the fraction form for various repeating decimals encountered in math problems or real-life situations.