From decimal to fraction
Any terminating decimal can be written exactly as a fraction. Fractions are often clearer than decimals in recipes, measurements in inches, probabilities and math homework, where 3/8 says more than 0.375. This calculator converts a decimal into a fraction in lowest terms and into a mixed number, with the percentage.
The method
- Write the decimal over a power of ten, one zero per decimal place: 1.375 = 1,375/1,000.
- Find the greatest common divisor (GCD) of the numerator and denominator: here, 125.
- Divide both by the GCD: 1,375 ÷ 125 = 11 and 1,000 ÷ 125 = 8, so 1.375 = 11/8.
- For a mixed number, divide the numerator by the denominator: 11 ÷ 8 = 1 remainder 3, so 11/8 = 1 3/8.
The calculator follows the same steps with up to six decimal places.
Worked example
Convert 1.375 to a fraction.
- Fraction in lowest terms: 11/8.
- Mixed number: 1 3/8.
- Percentage: 137.5%.
- Check: 11 ÷ 8 = 1.375.
Common decimals and their fractions
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.375 | 3/8 |
| 0.5 | 1/2 |
| 0.625 | 5/8 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
Eighths are worth memorizing in the US: tape measures, drill bits and wrenches are graduated in fractions of an inch, so 0.375 in is the 3/8 in mark.
Repeating decimals
Some fractions, like 1/3 = 0.333… or 2/7 = 0.285714…, give decimals that never end. With six decimal places, the calculator treats 0.333333 as 333,333/1,000,000, which is very close to 1/3 but not equal. To convert a repeating decimal exactly, use algebra: if x = 0.333…, then 10x = 3.333…, so 9x = 3 and x = 1/3. For 0.272727…, multiply by 100: 99x = 27, so x = 27/99 = 3/11.
Which fractions give terminating decimals
A fraction in lowest terms has a terminating decimal only if its denominator has no prime factors other than 2 and 5. That is why eighths, fifths and twentieths end neatly, while thirds, sixths and sevenths repeat.
Negative numbers
The sign carries over to the fraction: −0.75 = −3/4. The calculator keeps the sign on the numerator and the whole part.