How does the repeating decimal conversion work?

For a repeating decimal like 0.333..., the tool uses algebra: let x = 0.333..., then 10x = 3.333..., subtract to get 9x = 3, so x = 3/9 = 1/3. Similarly, for 0.1666..., let x = 0.1666..., then 100x = 16.666..., 10x = 1.666..., subtract to get 90x = 15, so x = 15/90 = 1/6.

What is a mixed number?

A mixed number combines a whole number and a proper fraction, like 1¾ (which equals 7/4). When the fraction value is greater than 1, the tool shows both the improper fraction (e.g., 7/4) and the mixed number (e.g., 1¾) for convenience.

Is the calculation accurate?

Yes, it uses exact rational arithmetic with JavaScript's BigInt for precise integer operations — no floating-point approximations. Terminating decimals are converted using powers of 10, and repeating decimals are solved algebraically. All results are reduced to their simplest form using the Euclidean algorithm (GCD).

Absolutely. This tool runs entirely in your browser. All calculations happen locally on your device. No data is sent to any server or third party. Your inputs and results never leave your computer.

Free Online Decimal to Fraction Calculator

Enter a Decimal

Supports terminating and repeating decimals. Use parentheses for repeating parts, e.g., 0.3(3) = 0.333...

Try these examples:

Enter a decimal and click "Convert"

📖 About Decimal to Fraction Conversion

Converting decimals to fractions is a fundamental math skill. This tool handles both types:

Terminating decimals — e.g., 0.75 = 75/100 = 3/4. Multiply by a power of 10 and simplify.
Repeating decimals — e.g., 0.333... = 1/3. Solved algebraically: x = 0.333..., 10x = 3.333..., 9x = 3, x = 1/3.

All results are reduced to simplest form using the Euclidean algorithm (GCD).

❓ FAQ

How do I input a repeating decimal?

Use parentheses around the repeating digit(s). Examples: 0.3(3) = 0.333..., 0.1(428571) = 0.142857142857..., 1.2(7) = 1.2777.... Both pure and mixed repeating decimals work.

Input format rules

Input must be a valid number. Can start with + or -. Must have at most one decimal point. Parentheses must be properly matched for repeating parts. Examples: 0.25 (terminating), 0.(142857) (pure repeating), 0.16(6) (mixed repeating).

How does simplification work?

The tool uses the Euclidean algorithm (GCD) to find the greatest common divisor of the numerator and denominator, then divides both by the GCD. For example, 42/56 has GCD 14, simplifying to 3/4.

What are mixed numbers?

When a fraction's value exceeds 1, it can be expressed as a mixed number (whole number + proper fraction). For example, 7/4 = 1¾. The tool displays both forms for convenience.

Is the result exact?

Yes, completely exact. The tool uses JavaScript BigInt for precise integer arithmetic — no floating-point rounding errors. Repeating decimals are solved via algebraic equations. Every result is mathematically exact.

🧮 Decimal to Fraction Calculator