About

This tool converts decimal numbers into their precise rational fraction equivalents. Unlike standard calculators that approximate values, this converter uses BigInt arithmetic to handle arbitrary precision, ensuring that even complex repeating decimals (e.g., 0.1(6)) are transformed into exact fractions (e.g., 16).

It distinguishes between terminating decimals (which have a finite number of digits) and repeating decimals (rational numbers with infinite recurring sequences). The result is automatically reduced to its simplest form using the Greatest Common Divisor (GCD) algorithm.

Formulas

For a terminating decimal x, count the decimal places d. The fraction is:

x = x × 10^d10^d

For a repeating decimal (e.g., 0.1(6) where 6 repeats):

Numerator = WholeSequence − NonRepeatingPart

Denominator = 9...9 (count of repeating digits) 0...0 (count of non-repeating digits)

Reference Data

Decimal	Fraction	Type
0.125	18	Terminating
0.333...	13	Repeating
0.1(6)	16	Repeating
0.75	34	Terminating
3.14159	314159100000	Approximation

Frequently Asked Questions

Use parentheses to denote the repeating part. For example, to input 0.1666..., type 0.1(6). The tool interprets the digits inside the brackets as the infinite recurring sequence.

If your input has many decimal places (e.g., 0.123456), the denominator becomes a power of 10 (1,000,000). The tool simplifies this if possible, but some numbers naturally have large prime factors.

Yes. Negative decimals will produce negative fractions. The negative sign is typically placed on the numerator or in front of the fraction.

The tool uses BigInt, meaning it is limited only by your browser's memory, not by the standard 15-digit limit of normal calculators.