Decimal to Fraction Converter
Convert any decimal to a simplified fraction using the place-value method — 0.375 becomes 375/1000, then 3/8 — with every GCD step shown, mixed numbers for values above 1, and the reverse fraction to decimal direction too.
Decimal → fraction
0.375 = 3/8
The decimal part .375 has 3 decimal places, so .375 = 375/1000
GCD(375, 1000) = 125
(375 ÷ 125)/(1000 ÷ 125) = 3/8
Honest note: a repeating decimal entered truncated (like 0.333 for 0.333…) gives an approximate fraction — 333/1000, not exactly 1/3.
Fraction → decimal
5/8 = 0.625
5 ÷ 8 = 0.625 (shown to at most 10 decimal places)
Common decimal–fraction conversions
| Decimal | Fraction | Note |
|---|---|---|
| 0.25 | 1/4 | exact |
| 0.333… | 1/3 | repeating — 0.333 is approximate |
| 0.5 | 1/2 | exact |
| 0.625 | 5/8 | exact |
| 0.666… | 2/3 | repeating — 0.667 is approximate |
| 0.75 | 3/4 | exact |
Frequently Asked Questions
- How do I convert a decimal to a fraction?
- Write the decimal digits over the matching power of 10, then simplify by the greatest common divisor. For 0.375: three decimal places means 375/1000, and dividing both by the GCD of 125 gives 3/8.
- How do I convert a fraction to a decimal?
- Divide the numerator by the denominator. For example, 5/8 = 5 ÷ 8 = 0.625.
- How are decimals greater than 1 handled?
- The whole-number part is kept aside and the decimal part is converted on its own, giving a mixed number. For 2.75, the 0.75 becomes 3/4, so the result is 2 3/4 (or 11/4 as an improper fraction).
- What about repeating decimals like 0.333…?
- A truncated repeating decimal gives an approximate fraction, not the exact one: 0.333 converts to 333/1000, which is close to but not exactly 1/3. This tool converts exactly what you type, so for repeating decimals treat the result as an approximation.
- Can every decimal be written as a fraction?
- Every terminating or repeating decimal can — those are the rational numbers. Irrational numbers like π or √2 never terminate or repeat, so no fraction represents them exactly.