Fraction to Decimal Calculator
Convert any fraction or mixed number to its decimal equivalent. Type the fraction naturally — for example 3/4 or 1 2/3 — and see the conversion worked out step by step, including whether the decimal terminates or repeats.
Convert Fraction to Decimal
Accepted: 3/4 · 1 2/3 · -5/8 · -2 1/4
Result
Step-by-Step Solution
How Fraction-to-Decimal Conversion Works
A fraction is really just a division problem written vertically. The fraction \(\dfrac{a}{b}\) means \(a \div b\). To find the decimal, you perform that division:
$$\dfrac{3}{4} = 3 \div 4 = 0.75$$Terminating vs. Repeating Decimals
Every fraction converts to either a terminating decimal (it ends) or a repeating decimal (one or more digits repeat infinitely).
A fraction in lowest terms produces a terminating decimal if and only if the denominator has no prime factors other than 2 and 5. This is because our decimal system is base 10, and 10 = 2 × 5.
| Fraction | Denominator factors | Result | Type |
|---|---|---|---|
| \(\frac{3}{4}\) | 2 × 2 | 0.75 | Terminating |
| \(\frac{1}{5}\) | 5 | 0.2 | Terminating |
| \(\frac{1}{3}\) | 3 | 0.333… | Repeating |
| \(\frac{1}{6}\) | 2 × 3 | 0.1666… | Repeating |
| \(\frac{1}{7}\) | 7 | 0.142857142857… | Repeating |
Mixed Numbers
A mixed number like \(2\,\dfrac{3}{4}\) is first converted to an improper fraction (\(\dfrac{11}{4}\)), and then the division is performed: \(11 \div 4 = 2.75\).
Alternatively, you can convert just the fractional part and add it to the whole number: \(2 + 0.75 = 2.75\).
Common Fraction-to-Decimal Conversions
| Fraction | Decimal | Percent |
|---|---|---|
| \(\frac{1}{2}\) | 0.5 | 50% |
| \(\frac{1}{3}\) | 0.3333… | 33.33% |
| \(\frac{2}{3}\) | 0.6666… | 66.67% |
| \(\frac{1}{4}\) | 0.25 | 25% |
| \(\frac{3}{4}\) | 0.75 | 75% |
| \(\frac{1}{5}\) | 0.2 | 20% |
| \(\frac{1}{8}\) | 0.125 | 12.5% |
| \(\frac{1}{10}\) | 0.1 | 10% |
Related Calculators
If you need to go in the other direction or do arithmetic with fractions, these tools will help:
- Decimal to Fraction Calculator — convert a decimal back to a simplified fraction
- Fraction Calculator — add, subtract, multiply, or divide any two fractions
- Simplify Fraction — reduce a fraction to its lowest terms
Frequently Asked Questions
- Why do some fractions produce repeating decimals?
- Our number system is base 10, so only fractions whose denominators (in simplest form) have 2 and 5 as their only prime factors will divide evenly. All other denominators produce remainders that cycle, creating repeating patterns.
- How do I convert a repeating decimal back to a fraction?
- Use the Decimal to Fraction Calculator. For repeating decimals you can also use algebra: if \(x = 0.\overline{3}\), then \(10x = 3.\overline{3}\), so \(9x = 3\) and \(x = \frac{1}{3}\).
- Does the result round?
- The decimal value is computed using JavaScript's 64-bit floating-point math, which is accurate to about 15 significant digits. For repeating decimals, this will display the repeating portion truncated at the floating-point precision limit.
- Can I convert negative fractions?
- Yes. Enter a minus sign before the fraction, e.g.
-3/4converts to-0.75.
