Decimal to Fraction Calculator
Convert any decimal value into a simplified fraction. Auto-detects common repeating decimals (1/3, 1/6, 1/9, etc.).
Reviewed & updated for 2026 · How we calculate
Common decimals to fractions
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.25 | 1/4 |
| 0.333... (repeating) | 1/3 |
| 0.375 | 3/8 |
| 0.4 | 2/5 |
| 0.5 | 1/2 |
| 0.6 | 3/5 |
| 0.625 | 5/8 |
| 0.666... (repeating) | 2/3 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
| 0.0625 | 1/16 |
The math behind decimal-to-fraction conversion
Every terminating decimal can be written as a fraction with a power of 10 in the denominator. 0.7 = 7/10. 0.07 = 7/100. 0.007 = 7/1000. The number of decimal places equals the number of zeros in the denominator. Then you simplify by dividing both top and bottom by their greatest common divisor (GCD).
Example: 0.375. Three decimal places → 375/1000. The GCD of 375 and 1000 is 125. Divide both: 375 ÷ 125 = 3, 1000 ÷ 125 = 8. So 0.375 = 3/8 in lowest terms. The Euclidean algorithm computes GCD efficiently: GCD(a, b) = GCD(b, a mod b), repeated until the remainder is zero.
Repeating decimals need algebra. To convert 0.272727... let x = 0.272727... Multiply by 100 (because the repeating block is two digits): 100x = 27.272727... Subtract the original: 99x = 27. So x = 27/99 = 3/11. The trick is always to multiply by 10^n where n is the length of the repeating block, then subtract to eliminate the infinite tail.
Why some fractions repeat and others don't
A fraction in lowest terms produces a terminating decimal if and only if its denominator's prime factorization contains only 2s and 5s. Why? Because our number system is base-10, and 10 = 2 × 5. Denominators of 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, all terminate. Denominators of 3, 6, 7, 9, 11, 12, 13, 14, all repeat.
1/3 = 0.333... never terminates because 3 has no factors of 2 or 5. The repeating block length equals the multiplicative order of 10 modulo the denominator, a deep number-theoretic property. 1/7 has a repeat length of 6 (0.142857 142857...). 1/17 repeats every 16 digits. 1/97 repeats every 96 digits. These mathematical patterns matter for cryptography and pseudorandom number generation.
Where you actually need these conversions
- US standard measurements: Rulers in inches use fractions (1/8, 1/4, 3/8, 1/2). Digital tools output decimals. Carpenters constantly convert: 0.625" = 5/8".
- Stock trading (pre-2001): Stocks once traded in eighths and sixteenths. 1/16 = $0.0625. Decimalization in 2001 ended this, but the conversion still matters for historical data.
- Music and time signatures: 0.5 beats = half note = 1/2. 0.25 = quarter note = 1/4. 0.125 = eighth note = 1/8. Music software displays both depending on context.
- Cooking conversions: A digital scale reads 0.75 cups; a measuring cup uses 3/4. 0.333 cup needs interpretation as 1/3 cup.
- Probability and statistics: A probability of 0.166666... is much more recognizable as 1/6 (one die face out of six).
FAQs
How do I convert a decimal to a fraction?
For terminating decimals: write the decimal over a power of 10, then simplify. Example: 0.625 = 625/1000 = 5/8 (after dividing both by 125). For repeating decimals: use algebra. Example: 0.333... = 1/3 (let x = 0.333..., 10x = 3.333..., 10x − x = 3, so 9x = 3, x = 1/3).
What is 0.75 as a fraction?
0.75 = 75/100 = 3/4 (simplified by dividing both numerator and denominator by 25).
What is 0.625 as a fraction?
0.625 = 625/1000 = 5/8 (after dividing by 125). The eighths series are: 1/8 = 0.125, 2/8 = 0.25, 3/8 = 0.375, 4/8 = 0.5, 5/8 = 0.625, 6/8 = 0.75, 7/8 = 0.875.
What is 0.333 repeating as a fraction?
0.333... (with 3 repeating forever) = 1/3 exactly. For 0.66... = 2/3. For 0.999... = 1 (it's a real mathematical fact that 0.999... equals 1 exactly).
How do I simplify a fraction?
Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. Example: 24/36 → GCD is 12 → 24/12 = 2, 36/12 = 3 → simplified to 2/3.