Decimal to Fraction Calculator
History
Your results will appear here. Tap Use on any of them to carry it into the next calculation, in this calculator or another one. History is kept while this tab is open.
To write a decimal as a fraction, put its digits over 10, 100 or 1000 (one zero for each decimal place), then divide both numbers by their greatest common factor: 0.75 = 75/100 = 3/4. This decimal to fraction converter also goes the other way: pick Fraction → Decimal.
How to Convert a Decimal to a Fraction
To convert a decimal to a fraction, start by counting the digits after the decimal point. That count sets the denominator.
- Drop the decimal point and write the digits over 1 followed by that many zeros. 0.75 has two decimal places, so 0.75 = 75/100.
- Divide the numerator and the denominator by their greatest common factor (GCF), the largest number that divides both. For 75 and 100 it's 25, so 75/100 = 3/4. This is the same step as when you simplify fractions.
- If the decimal is greater than 1, you can also write the answer as a mixed number: 2.125 = 2125/1000 = 17/8 = 2 1/8.
A negative decimal works the same way. Convert it without the minus sign, then put the sign back in front: −0.5 = −5/10 = −1/2.
The calculator shows this step in the line under the result: 75/100 = 3/4 · GCF 25.
Repeating Decimals
Typing 0.333 gives 333/1000. That's a different number from 0.333…, which never ends. To change a repeating decimal to a fraction, put the repeating part in Repeating digits: Decimal 0, Repeating digits 3, and you get 1/3.
The rule behind it: a block of p repeating digits goes over p nines, so 0.333… = 3/9 = 1/3. If the repeat starts a few digits in, as in 0.1666…, enter 0.1 in Decimal and 6 in Repeating digits. The answer is 1/6.
A long decimal like 2.28571428571 still ends where you stop typing, so it converts to 228571428571/100000000000. Enter 2 with Repeating digits 285714 and you get 16/7 = 2 2/7.
Fraction to Decimal
To turn a fraction into a decimal, divide the numerator by the denominator: 7/8 = 7 ÷ 8 = 0.875.
The decimal ends only if the denominator, after you divide out every common factor, has no prime factors other than 2 and 5. Any other denominator gives a repeating decimal: 1/7 = 0.142857… For a mixed number, add the whole part to the decimal of the fraction: 1 3/4 = 1 + 0.75 = 1.75.
To use this as a fraction to decimal calculator, pick Fraction → Decimal. A repeating answer gets a bar over the repeating digits, with ≈ 0.142857142857 underneath (12 significant digits).
Multiply a decimal by 100 and you have a percent: 0.75 is 75%. For percent problems, use the percentage calculator.
Decimal to Fraction Chart
Common fractions and their decimals. Digits under a bar repeat forever.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.3 |
| 2/3 | 0.6 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 2/5 | 0.4 |
| 3/5 | 0.6 |
| 4/5 | 0.8 |
| 1/6 | 0.16 |
| 5/6 | 0.83 |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 7/8 | 0.875 |
| 1/10 | 0.1 |
| 3/10 | 0.3 |
| 7/10 | 0.7 |
| 9/10 | 0.9 |
| 1/12 | 0.083 |
| 5/12 | 0.416 |
| 7/12 | 0.583 |
| 11/12 | 0.916 |
| 1/16 | 0.0625 |
| 3/16 | 0.1875 |
| 5/16 | 0.3125 |
| 7/16 | 0.4375 |
| 9/16 | 0.5625 |
| 11/16 | 0.6875 |
| 13/16 | 0.8125 |
| 15/16 | 0.9375 |
Examples
Each row is one conversion, as the display shows it. The last one goes the other way, from a fraction to a decimal.
| You enter | Result | Line under the result |
|---|---|---|
| 0.75 | 3/4 | 75/100 = 3/4 · GCF 25 |
| 1.5 | 3/2 = 1 1/2 | 15/10 = 3/2 · GCF 5 |
| 0, Repeating digits 3 | 1/3 | (3 − 0)/9 = 3/9 = 1/3 · GCF 3 |
| −0.5 | −1/2 | −5/10 = −1/2 · GCF 5 |
| 7/8, Fraction → Decimal | 0.875 | — |
To add, subtract, multiply or divide the result, send it to the fraction calculator with Use result. It also goes into fields that take a plain number, such as the ones in the scientific calculator, where a fraction arrives as its decimal.
FAQ
How do you change a decimal number to a fraction?
Write its digits over 10, 100 or 1000, one zero per decimal place, and divide both numbers by their greatest common factor: 0.75 = 75/100 = 3/4. The steps are in How to Convert a Decimal to a Fraction.
What is 0.8 as a fraction?
0.8 is 8/10, and dividing both numbers by 2 gives 4/5.
What is 7/8 as a decimal?
7/8 is 0.875: divide 7 by 8.
How do you convert a repeating decimal to a fraction?
Enter the digits before the repeat in Decimal and the repeating part in Repeating digits. By hand, a block of p repeating digits goes over p nines: 0.333… = 3/9 = 1/3. More in Repeating Decimals.
How do I convert a decimal to a fraction without a calculator?
On paper, the steps are the same. 2.125 has three decimal places, so write 2125/1000. The greatest common factor of 2125 and 1000 is 125, which leaves 17/8, or 2 1/8.