Fraction to Decimal Calculator
Convert any fraction to a decimal and percentage, and simplify it.
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Enter a numerator and a denominator and this calculator converts the fraction to a decimal and a percentage, and reduces it to lowest terms. For example, 18/24 becomes 0.75, 75% and 3/4 in one step.
What the three results show
- Decimal: numerator ÷ denominator, rounded to at most six decimal places.
- Percentage: the decimal × 100, rounded to at most four decimal places.
- Simplified: both numbers divided by their highest common factor. For 18/24 the HCF is 6, giving 3/4.
Improper fractions (top larger than bottom) and negative values work normally. A denominator of 0 shows an error, because division by zero is undefined.
Simplifying does not change the value, only the way it is written. 18/24, 6/8 and 3/4 all describe the same point on the number line, which is why they share one decimal. Teachers usually expect the lowest-terms version as the final answer, and it also makes comparing fractions easier: once 18/24 is shown as 3/4, it is obvious that it is bigger than 2/3 (0.666667) and smaller than 4/5 (0.8).
Worked examples
| Fraction | Decimal | Percentage |
|---|---|---|
| 5/8 | 0.625 | 62.5% |
| 1/3 | 0.333333 | 33.3333% |
| 2/3 | 0.666667 | 66.6667% |
| 7/3 | 2.333333 | 233.3333% |
| 45/60 | 0.75 | 75% |
The last row is a typical marks question: 45 out of 60 is 75%. For a full mark sheet across several subjects, the exam marks percentage calculator totals everything for you.
Terminating or repeating decimals
Whether a fraction ends neatly depends only on its denominator once it is in lowest terms. If the denominator's prime factors are just 2s and 5s, the decimal terminates: 5/8 has 8 = 2 × 2 × 2, so it stops at 0.625. Any other prime factor produces a repeating decimal. 1/3 is 0.333… forever, and 1/7 repeats the six-digit block 142857.
Because the calculator rounds to six places, 2/3 appears as 0.666667 with the last digit rounded up. In school answers, write repeating decimals with a bar over the repeating digits, or keep the fraction, since it is exact while any rounded decimal is not.
Tips for tricky inputs
- Mixed numbers: convert 2 1/3 to an improper fraction first. Multiply the whole number by the denominator and add the numerator: (2 × 3 + 1)/3 = 7/3.
- Decimals inside the fraction: the Simplified line needs whole numbers. For 1.5/4, multiply top and bottom by 2 and enter 3/8.
- Decimal back to a fraction: write the decimal over a power of ten and let the tool simplify it. 0.75 is 75/100, which reduces to 3/4.
- Measurements: drill bits and spanners are often labelled in fractional inches. 5/8 inch is 0.625 inch, and multiplying by 25.4 gives 15.875 mm.
To compare two quantities rather than convert one, the ratio calculator solves proportions such as 3:4 = 12:x.