Fraction to Decimal Converter

Fraction to Decimal Converter

Convert fractions to decimals with exact repeating decimal detection and notation. Enter a simple fraction or mixed number and instantly see the decimal value, simplified fraction, percentage, and whether the decimal terminates or repeats. Includes step-by-step long division visualization, reverse decimal-to-fraction conversion, and fraction arithmetic operations.

How to Use

Enter a numerator and denominator, or enable mixed number mode to include a whole number. Click common fraction quick buttons for frequently used values. The converter instantly shows the decimal result with repeating cycle notation, simplified fraction, mixed number form, and percentage. View the long division visualization to see how the decimal is computed step by step. Use reverse mode to convert a decimal back to a fraction, or perform fraction arithmetic with two fractions.

Features

• Repeating Decimal Detection — Automatically detects repeating cycles using long division remainder tracking. Shows repeating digits with overbar notation and parentheses notation (e.g., 1/7 = 0.142857 with repeating mark).
• Fraction Simplification — Reduces fractions to lowest terms using the GCD algorithm. Shows both original and simplified forms.
• Mixed Number Support — Enter mixed numbers (e.g., 2 1/3) and convert improper fractions to mixed number form automatically.
• Long Division Visualization — Step-by-step display of the long division process with remainders at each step. Highlights where a remainder repeats to show the cycle start.
• Reverse Conversion — Enter a decimal to find the exact fraction. Handles terminating decimals and repeating decimals entered with notation like 0.(3) or 0.333… Optional max denominator limit.
• Fraction Operations — Add, subtract, multiply, and divide two fractions with simplified results shown as both fraction and decimal.
• Quick Reference — Common fractions table with decimal and percentage equivalents for values like 1/2, 1/3, 1/4, 1/8, 2/3, 3/4, and more.

Repeating Decimals

A fraction produces a terminating decimal when the denominator (after simplification) has only factors of 2 and 5. All other fractions produce repeating decimals. For example, 1/4 = 0.25 (terminating) because 4 = 2 x 2, but 1/3 = 0.333… (repeating) because 3 has no factors of 2 or 5. The length of the repeating cycle is always less than the denominator — 1/7 has a 6-digit cycle (142857), which is the maximum for a denominator of 7.