Fraction to Decimal Converter
Convert any fraction or mixed number to its decimal and percentage equivalent
What Does This Tool Do?
The Fraction to Decimal Converter takes any fraction and instantly shows its decimal equivalent, percentage value, and whether the decimal terminates or repeats. For repeating decimals, the repeating digit pattern is clearly highlighted so you can see exactly which digits cycle. The tool supports mixed number input, allowing you to enter a whole number alongside the fraction. It is ideal for homework help, quick reference, and building intuition about the relationship between fractions and decimals.
How to Use
- Enter the numerator and denominator of your fraction in the input fields.
- Optionally enter a whole number to convert a mixed number like 2 3/4.
- View the results that update instantly: the decimal value, percentage, whether it terminates or repeats, and the repeating pattern if applicable.
- Check the repeating pattern card for repeating decimals. The overlined digits show exactly which digits repeat infinitely.
Common Fractions Reference
| Fraction | Decimal | Percentage | Type |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Terminating |
| 1/3 | 0.333... | 33.333...% | Repeating |
| 1/4 | 0.25 | 25% | Terminating |
| 1/5 | 0.2 | 20% | Terminating |
| 1/6 | 0.1666... | 16.666...% | Repeating |
| 1/7 | 0.142857... | 14.2857...% | Repeating |
| 1/8 | 0.125 | 12.5% | Terminating |
| 1/9 | 0.111... | 11.111...% | Repeating |
| 1/10 | 0.1 | 10% | Terminating |
| 2/3 | 0.666... | 66.666...% | Repeating |
| 3/4 | 0.75 | 75% | Terminating |
| 7/8 | 0.875 | 87.5% | Terminating |
FAQ
How does the tool determine if a decimal repeats?
It uses long division to track remainders. If a remainder appears a second time, the digits between the two occurrences form the repeating cycle. A fraction in lowest terms terminates only when the denominator has no prime factors other than 2 and 5.
What does the overline on the digits mean?
The overline indicates the repeating block. For example, 0.142857 means the digits 142857 repeat forever: 0.142857142857142857...
Can I enter improper fractions like 7/4?
Yes. The tool accepts any positive numerator and denominator. An improper fraction like 7/4 will display as 1.75, which is the same as the mixed number 1 3/4.
What happens if I enter 0 as the denominator?
Division by zero is undefined in mathematics. The tool will display an error message asking you to enter a denominator greater than zero.
How long can the repeating cycle be?
The maximum cycle length for a fraction 1/n is n-1 digits. For example, 1/7 has a 6-digit cycle (142857). The tool computes up to 2000 digits to find the pattern, which covers virtually all practical cases.