Decimal to Fraction Converter

How to Use This Calculator

1. Enter any decimal number (e.g. 0.75 or 1.333).
2. The simplified fraction and mixed number appear instantly.
3. Use Fraction to Decimal tab for the reverse conversion.
4. Use Repeating Decimal tab for 0.333... type inputs.
5. The Professional tab shows the nearest standard fractions (1/2, 1/4, 1/8, 1/16).

Formula

Example

Frequently Asked Questions

• How do I convert 0.75 to a fraction? ▼
  To convert 0.75 to a fraction: write 0.75 as 75/100 (the decimal has 2 places, so denominator = 100). Then simplify by finding the Greatest Common Divisor (GCD) of 75 and 100. Since GCD(75, 100) = 25, divide both by 25: 75/100 = 3/4. So 0.75 = 3/4. Other common decimal-to-fraction conversions: 0.5 = 1/2; 0.25 = 1/4; 0.125 = 1/8; 0.333... = 1/3; 0.2 = 1/5; 0.4 = 2/5; 0.6 = 3/5; 0.8 = 4/5; 0.1 = 1/10; 0.625 = 5/8. To verify: divide the numerator by the denominator and confirm you get the original decimal. 3 ÷ 4 = 0.75 ✓. Fractions that have only 2s and 5s as factors in the denominator (when in lowest terms) will produce terminating decimals; all others produce repeating decimals.
• How do I convert a repeating decimal to a fraction? ▼
  For a simple repeating decimal like 0.333..., use algebra. Let x = 0.333.... Multiply both sides by 10: 10x = 3.333.... Subtract: 10x − x = 3.333... − 0.333... → 9x = 3 → x = 3/9 = 1/3. For 0.142857142857... (recurring 6 digits): let x = 0.142857...; multiply by 10⁶ = 1,000,000; then 1,000,000x = 142857.142857...; subtract: 999,999x = 142857; x = 142857/999999 = 1/7. General rule: if n digits repeat, multiply by 10ⁿ before subtracting. For a partially repeating decimal like 0.16666... (0.1 then 6 repeating): let x = 0.16666...; 10x = 1.6666...; 100x = 16.6666...; 100x − 10x = 15; 90x = 15; x = 15/90 = 1/6.
• How do I convert 1.6 to a fraction? ▼
  1.6 = 1 + 0.6 = 1 + 6/10 = 1 + 3/5 = 8/5 as an improper fraction. As a mixed number: 1 and 3/5 (written "1 3/5"). Verification: 8 ÷ 5 = 1.6 ✓. Method: write the decimal part as a fraction (0.6 = 6/10 = 3/5), add to the whole number: 1 + 3/5 = 5/5 + 3/5 = 8/5. Other examples: 1.25 = 5/4 (mixed: 1 1/4); 1.5 = 3/2 (mixed: 1 1/2); 1.75 = 7/4 (mixed: 1 3/4); 2.333... = 7/3 (mixed: 2 1/3); 3.125 = 25/8 (mixed: 3 1/8). When a decimal is greater than 1, you can choose between an improper fraction (like 8/5) or a mixed number (like 1 3/5) — both are correct representations. Mixed numbers are preferred in everyday contexts; improper fractions are preferred in mathematical calculations.
• What is a mixed number? ▼
  A mixed number combines a whole number and a proper fraction, such as 2 3/4 (read "two and three-quarters"). The whole number part represents complete units; the fraction represents the remaining partial unit. Every mixed number can be converted to an improper fraction: multiply the whole number by the denominator, add the numerator, keep the same denominator. Example: 2 3/4 = (2×4 + 3)/4 = 11/4. To convert back from improper to mixed: divide numerator by denominator; the quotient is the whole number, remainder is the new numerator. 11 ÷ 4 = 2 remainder 3 → 2 3/4. Mixed numbers appear naturally in measurements: a recipe might call for 1 1/2 cups; a board might be 3 5/8 inches wide. When performing arithmetic with mixed numbers, convert to improper fractions first for multiplication/division.
• How do I simplify a fraction? ▼
  To simplify (reduce) a fraction, divide both numerator and denominator by their Greatest Common Divisor (GCD). Steps: find GCD(numerator, denominator), then divide both by that GCD. Example: simplify 18/24. Find GCD(18, 24): factors of 18 = 2×3²; factors of 24 = 2³×3; GCD = 2×3 = 6. Divide: 18/6 = 3, 24/6 = 4. Result: 3/4. Alternative method (Euclidean algorithm): GCD(24, 18) → 24 = 1×18 + 6 → GCD(18, 6) → 18 = 3×6 + 0 → GCD = 6. A fraction is in lowest terms (fully simplified) when GCD(numerator, denominator) = 1. Common simplifications: 4/8 = 1/2; 6/9 = 2/3; 15/25 = 3/5; 12/18 = 2/3; 100/250 = 2/5. Never change the value of a fraction when simplifying — only the representation changes.

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