Decimal to Fraction Calculator

Convert any decimal number to a fraction, simplified fraction, or mixed number instantly. Supports terminating and repeating decimals.

Convert Decimal to Fraction

How to Convert a Decimal to a Fraction

Step 1: Count the decimal places (n). Write the decimal digits as the numerator and 10n as the denominator.

Step 2: Simplify by dividing both numerator and denominator by their Greatest Common Divisor (GCD).

Example: 0.75 → 75/100 → GCD(75,100) = 25 → 3/4

Mixed Numbers: If the decimal is greater than 1, separate the whole part and convert the decimal part. e.g. 2.5 → 2 + 1/2 = 2½

Repeating Decimals: For repeating decimals like 0.333..., use the algebraic method: x = 0.333..., 10x = 3.333..., subtract to get 9x = 3, so x = 3/9 = 1/3.

Frequently Asked Questions

For a repeating decimal like 0.333..., set x = 0.333... and multiply both sides by 10 to get 10x = 3.333... Subtract the first from the second: 9x = 3, so x = 3/9 = 1/3. For longer repeating blocks, multiply by the appropriate power of 10 to shift the repeat. This calculator handles standard terminating decimals; for complex repeating decimals, the algebraic method above is most reliable.

A simplified (or reduced) fraction is one where the numerator and denominator share no common factors other than 1. For example, 4/8 simplifies to 1/2 because both 4 and 8 are divisible by 4. To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). A fraction is in its simplest form when GCD(numerator, denominator) = 1.

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