Decimal to Fraction Converter
Type a decimal such as 0.375 and get the simplified fraction (3/8) with every step: the place-value fraction, the greatest common divisor and the reduced result, plus a mixed number for values above 1. A second box converts any fraction to a decimal. Free, no sign-up.
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)
How to Use the Decimal to Fraction Converter
- 1. Decimal to fraction. Type a decimal in the first box — 0.375, 2.75 or -0.5. The headline shows the fraction in lowest terms and, above 1, the mixed number and the improper fraction.
- 2. Follow the steps. The lines beneath show the decimal part as a fraction over a power of 10, the greatest common divisor, and the division that reduces it.
- 3. Fraction to decimal. In the second section, enter a whole-number numerator and denominator. The decimal appears to at most ten places.
- 4. Mind the limits. Up to ten decimal places are accepted, and a leading-dot decimal such as .5 or -.5 is read as 0.5 or -0.5.
How a Decimal Becomes a Fraction
Each decimal place is a power of ten, so a decimal with n places is a fraction over 10n: 0.375 has three places, so it is 375/1000. That fraction is correct but not simplified. Divide the top and bottom by their greatest common divisor — here 125 — and you get 3/8. For a number above 1, the whole part stays aside: 2.75 is 2 and 75/100, which reduces to 2 3/4, or 11/4 as an improper fraction (2 × 4 + 3 = 11).
| Decimal | Over a power of 10 | GCD | Simplified | Mixed / improper |
|---|---|---|---|---|
| 0.375 | 375/1000 | 125 | 3/8 | — |
| 0.0625 | 625/10000 | 625 | 1/16 | — |
| 0.666 | 666/1000 | 2 | 333/500 | — |
| 0.333 | 333/1000 | 1 | 333/1000 | — |
| 2.75 | 75/100 | 25 | 3/4 | 2 3/4 = 11/4 |
| 1.5 | 5/10 | 5 | 1/2 | 1 1/2 = 3/2 |
| -0.25 | 25/100 | 25 | −1/4 | — |
Repeating Decimals
The converter turns exactly what you type into a fraction. A truncated repeating decimal is therefore not recognized: 0.333 becomes 333/1000, close to but not equal to 1/3, and 0.3333333333 becomes 3333333333/10000000000. To find the exact fraction for a repeating decimal, use algebra. Let x = 0.333…; then 10x = 3.333…, and subtracting gives 9x = 3, so x = 1/3. For a two-digit repeat, multiply by 100: 0.2727… gives 99x = 27, so x = 27/99 = 3/11. Every terminating or repeating decimal is a fraction; irrational numbers such as π and √2 are not, and any fraction for them is an approximation.
Fraction to Decimal
Divide the numerator by the denominator. A fraction in lowest terms gives a terminating decimal only if its denominator has no prime factors other than 2 and 5: 5/8 = 0.625 and 7/16 = 0.4375 terminate, while 1/3 = 0.3333333333, 2/3 = 0.6666666667 and 1/7 = 0.1428571429 repeat and are cut at ten places by the tool.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/8 | 0.125 | 5/8 | 0.625 |
| 1/4 | 0.25 | 3/4 | 0.75 |
| 3/8 | 0.375 | 7/8 | 0.875 |
| 1/5 | 0.2 | 4/5 | 0.8 |
| 1/16 | 0.0625 | 15/16 | 0.9375 |
Typing decimals
A single comma is read as a decimal mark, so 1,5 is 1.5 and 1,234 is 1.234. A leading dot is fine: .5 is read as 0.5.
Which Tool Do You Need?
| You want to… | Use |
|---|---|
| Convert a decimal to a fraction, or one fraction to a decimal | This converter |
| Add, subtract, multiply or divide fractions and mixed numbers | Fraction Calculator |
| Turn a decimal into a percentage or find a percent of a number | Percentage Calculator |
| Simplify a ratio or solve a proportion | Ratio Calculator |
| Round a decimal to a set number of places | Rounding Calculator |
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 gives 375/1000, and dividing both numbers by 125 gives 3/8.
- How do I convert a fraction to a decimal?
- Divide the numerator by the denominator: 5/8 = 5 ÷ 8 = 0.625. Enter the two numbers in the Fraction to decimal section, and the result is shown to at most ten decimal places.
- How are decimals greater than 1 handled?
- The whole 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. The converter shows both.
- 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, not 1/3. Use the algebra shown above — multiply by 10 or 100, subtract, and solve — to find the exact fraction.
- How many decimal places can I enter?
- Up to ten, not counting trailing zeros, so 12.050 is treated as 12.05. A longer decimal gets a message asking you to shorten it.
- Can every decimal be written as a fraction?
- Every terminating or repeating decimal can; those are the rational numbers. Irrational numbers such as π and √2 never terminate or repeat, so no fraction represents them exactly.