Fraction to Decimal Converter
This converter works in both directions. Switch to “Fraction → Decimal” to turn any fraction into its decimal value by dividing the numerator by the denominator, or to “Decimal → Fraction” to express a decimal number as a reduced fraction. Everything updates as you type, so you can check homework answers, convert measurements for cooking or woodworking, or simply understand how a number looks in either form. The result is always shown in its simplest terms.
Result
The fraction is always shown reduced by dividing the numerator and denominator by their greatest common divisor (GCD).
Publicidad
How it works
To convert a fraction to a decimal you divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce terminating decimals while others repeat, so the value is rounded for clarity. To convert a decimal to a fraction, the tool counts how many digits sit after the decimal point and writes the number over the matching power of ten — 0.75 becomes 75/100. It then finds the greatest common divisor (GCD) of the numerator and denominator with the Euclidean algorithm and divides both by it, so 75/100 reduces to 3/4. Whole numbers simply become the number over 1. To do the division by hand you use long division: divide the numerator by the denominator and keep bringing down zeros after the decimal point. With 1/4 the division stops quickly (0.25) because the remainder reaches zero; with 1/3 the remainder repeats forever and gives 0.333… A fraction in lowest terms produces a terminating decimal only when its denominator breaks down into just the factors 2 and 5 (like 2, 4, 5, 8, 10 or 20); if any other prime factor appears (3, 7, 11…), the decimal repeats. That is why 1/8 terminates and 1/6 does not.
Common fractions and their decimal value
These are the conversions that show up most in school, cooking and measurements. A fraction gives a terminating decimal when its reduced denominator has only the factors 2 and 5; otherwise the decimal repeats, and the three dots mean the digits go on forever:
| Fraction | Decimal | Type |
|---|---|---|
| 1/2 | 0.5 | terminating |
| 1/3 | 0.333… | repeating |
| 2/3 | 0.666… | repeating |
| 1/4 | 0.25 | terminating |
| 3/4 | 0.75 | terminating |
| 1/5 | 0.2 | terminating |
| 2/5 | 0.4 | terminating |
| 1/6 | 0.1666… | repeating |
| 5/6 | 0.8333… | repeating |
| 1/7 | 0.142857… | repeating |
| 1/8 | 0.125 | terminating |
| 3/8 | 0.375 | terminating |
| 5/8 | 0.625 | terminating |
| 1/9 | 0.111… | repeating |
| 1/10 | 0.1 | terminating |
Publicidad
Preguntas frecuentes
- How do I convert a fraction to a decimal?
- Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75 and 1/8 = 0.125. If the division does not end, the decimal repeats, like 1/3 = 0.3333… This converter does the division for you and rounds the result for readability.
- How do I convert a decimal to a fraction?
- Write the decimal over the power of ten that matches its digits after the point, then reduce. 0.75 has two decimals, so it is 75/100, which simplifies to 3/4. 0.2 is 2/10 = 1/5. Whole numbers such as 5 become 5/1.
- What is 0.75 as a fraction?
- 0.75 equals 3/4. There are two digits after the decimal point, so you start with 75/100, then divide both numbers by their greatest common divisor, which is 25, giving 3/4.
- Does the converter simplify the fraction automatically?
- Yes. Any fraction result is reduced to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). So 50/100 is shown as 1/2, not left unreduced.
- Can it handle repeating decimals like 0.333…?
- The tool converts the decimal you actually type. If you enter 0.333 it returns 333/1000, because it treats the value as an exact terminating decimal. To get 1/3 you would need to enter the fraction directly in the “Fraction → Decimal” mode.
- Why does 1/3 never end?
- Because when you divide 1 by 3 the remainder is always 1 again, so the 3 repeats forever: 0.333… A fraction in lowest terms gives a terminating decimal only if its denominator factors into just 2 and 5; 3 does not meet that condition, which is why 1/3, 1/6 and 1/9 repeat while 1/2, 1/4 and 1/8 terminate.