Fraction to Decimal Calculator
Convert any fraction to a decimal, percentage, and simplified form in one click. Enter the numerator and denominator below.
How Fraction Conversion Works
Converting a fraction to a decimal is simple: divide the numerator (top number) by the denominator (bottom number). The result is either a terminating decimal (it ends) or a repeating decimal (a sequence of digits repeats forever). Whether a fraction terminates depends entirely on the prime factorization of its denominator in lowest terms.
To convert to a percentage, multiply the decimal by 100. So 3/8 = 0.375 = 37.5%. To simplify the fraction, divide both numerator and denominator by their Greatest Common Divisor (GCD). The fraction 12/16 simplifies to 3/4 because GCD(12, 16) = 4.
Common Fractions Reference Table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/8 | 0.125 | 12.5% |
| 5/8 | 0.625 | 62.5% |
Terminating vs. Repeating Decimals
A fraction in lowest terms produces a terminating decimal if and only if the denominator has no prime factors other than 2 and 5. This is because our decimal system is base-10 (= 2 × 5). Denominators of 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, etc. all produce terminating decimals.
Any denominator containing 3, 7, 11, 13, 17, 19, or any prime other than 2 and 5 will produce a repeating decimal. Fractions like 1/3 (0.333...) and 1/7 (0.142857142857...) are mathematically exact — the repeating decimal is their true value, not an approximation. When you need exactness in calculations, use the fraction form rather than a rounded decimal.
Frequently Asked Questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. For 1/3 = 1 ÷ 3 = 0.3333... (repeating). Some fractions convert to terminating decimals (they end); others create repeating decimals (a pattern that repeats forever). Fractions whose denominators have only 2 and 5 as prime factors produce terminating decimals. Fractions with any other prime factors in the denominator produce repeating decimals.
How do you convert a decimal to a fraction?
For terminating decimals: write the decimal as a fraction with the appropriate power of 10 in the denominator, then simplify. 0.75 = 75/100 = 3/4. 0.125 = 125/1000 = 1/8. For repeating decimals: use algebra. Let x = 0.333... Multiply both sides by 10: 10x = 3.333... Subtract: 9x = 3, so x = 3/9 = 1/3. For 0.142857142857... (repeating), let x = 0.142857..., 999999x = 142857, x = 142857/999999 = 1/7.
What fractions create repeating decimals?
Any fraction in lowest terms where the denominator has a prime factor other than 2 or 5 will produce a repeating decimal. Common examples: 1/3 = 0.333..., 1/6 = 0.1666..., 1/7 = 0.142857142857..., 1/9 = 0.111..., 1/11 = 0.090909... The length of the repeating block (period) depends on the denominator. 1/7 has a 6-digit repeating block. 1/97 would have up to a 96-digit repeating block — because the maximum period of 1/n is n−1 digits.
What are the most common fraction to decimal conversions?
Memorizing these saves time: 1/2 = 0.5, 1/3 = 0.333..., 1/4 = 0.25, 1/5 = 0.2, 1/6 = 0.1666..., 1/7 = 0.142857..., 1/8 = 0.125, 1/9 = 0.111..., 1/10 = 0.1, 3/4 = 0.75, 2/3 = 0.666..., 5/8 = 0.625, 7/8 = 0.875. For percentages: multiply the decimal by 100. So 3/4 = 0.75 = 75%, and 1/3 = 0.333... ≈ 33.3%.