Fraction to Decimal Calculator
Turn any fraction into a decimal and a percentage, simplify it to lowest terms, and see the mixed-number form.
A fraction is a division: 3/8 means 3 ÷ 8 = 0.
How the fraction to decimal calculator works
A fraction is a division: 3/8 means 3 ÷ 8 = 0.375. To simplify, divide numerator and denominator by their greatest common divisor. A fraction whose reduced denominator has only the prime factors 2 and 5 terminates; any other denominator gives a repeating decimal.
Formula: decimal = numerator ÷ denominator; simplified = (n ÷ gcd) / (d ÷ gcd)
Worked examples
| Inputs | Decimal | Note |
|---|---|---|
| 3/8 | 0.375 | terminates |
| 2/3 | 0.6666666667 | repeats: 0.666… |
| 22/7 | 3.1428571429 | mixed number 3 1/7 |
FAQFrequently asked questions
How do I convert a fraction to a decimal by hand?
Divide the top number by the bottom number with long division. 3 ÷ 8 = 0.375.
Why do some fractions repeat forever?
A decimal terminates only when the reduced denominator is made of 2s and 5s (the factors of 10). 1/3, 1/6 and 1/7 repeat.
How do I simplify a fraction?
Divide both parts by their greatest common divisor: 6/8 → 3/4.
What is a mixed number?
A whole number plus a proper fraction: 22/7 = 3 1/7.
How do I turn a fraction into a percentage?
Convert to a decimal and multiply by 100: 3/8 = 0.375 = 37.5%.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.