Fraction to Decimal Converter
Enter a numerator and denominator (and an optional whole number for a mixed fraction) to convert it to a decimal. The result updates as you type, the step-by-step long division panel shows exactly how the conversion works, and a precision selector lets you round to between 0 and 10 decimal places.
Formula
Worked example
Converting 3/4: divide 3 by 4 to get 0.75. Since 4 = 2², its only prime factor is 2, so the decimal terminates. GCD(3, 4) = 1, so the fraction is already in lowest terms. As a percentage: 0.75 × 100 = 75%.
How to convert a fraction to a decimal
Converting a fraction to a decimal is straightforward: divide the numerator (top number) by the denominator (bottom number). For example, 3/4 becomes 0.75 because 3 divided by 4 equals 0.75. You can do this with long division, a calculator, or by finding an equivalent fraction whose denominator is a power of 10. When the denominator is already 10, 100, or 1000, conversion is instant: 3/10 = 0.3, 7/100 = 0.07, and 13/1000 = 0.013. For denominators that can be converted to powers of 10 by multiplication, such as 1/4 (multiply top and bottom by 25 to get 25/100 = 0.25), this method is often faster than long division.
Terminating vs. repeating decimals
Every fraction with integer numerator and denominator produces either a terminating decimal (one that ends, like 0.25) or a repeating decimal (one whose digits eventually cycle, like 0.333...). The denominator determines which type you get after the fraction is simplified to lowest terms. If the simplified denominator has only 2 and 5 as prime factors (for example, 4 = 2², 20 = 4 x 5, 25 = 5²), the decimal terminates. Any other prime factor - 3, 7, 11, 13, and so on - produces a repeating decimal. The repeating block is written with a bar above the cycling digits, or shown as "..." in text form. For example, 1/3 = 0.333... (repeating 3), 1/7 = 0.142857142857... (repeating block of six digits), and 1/6 = 0.1666... (repeating 6).
Converting mixed numbers
A mixed number combines a whole part and a proper fraction, such as 2 3/4. To convert it to a decimal, first convert to an improper fraction: multiply the whole number by the denominator and add the numerator (2 × 4 + 3 = 11), giving 11/4. Then divide 11 by 4 to get 2.75. Equivalently you can convert the fractional part alone (3/4 = 0.75) and add the whole number (2 + 0.75 = 2.75). Both routes give the same answer. The calculator above handles this automatically when you select the "Mixed number" option.
Simplifying before converting
Simplifying a fraction before converting can make the arithmetic easier. Divide the numerator and denominator by their greatest common divisor (GCD). For 6/8, the GCD is 2, giving 3/4 - and dividing 3 by 4 is simpler than dividing 6 by 8. Both give 0.75. Simplifying also helps identify whether the decimal will terminate: once 6/8 is reduced to 3/4, you can see the denominator (4 = 2²) has only factors of 2, confirming the decimal terminates.
Common fraction to decimal conversions
| Fraction | Decimal | Percentage | Decimal type |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Terminating |
| 1/3 | 0.333... | 33.33...% | Repeating |
| 1/4 | 0.25 | 25% | Terminating |
| 1/5 | 0.2 | 20% | Terminating |
| 1/6 | 0.1666... | 16.66...% | Repeating |
| 1/7 | 0.142857... | 14.285...% | Repeating |
| 1/8 | 0.125 | 12.5% | Terminating |
| 1/9 | 0.111... | 11.11...% | Repeating |
| 1/10 | 0.1 | 10% | Terminating |
| 1/16 | 0.0625 | 6.25% | Terminating |
| 1/32 | 0.03125 | 3.125% | Terminating |
| 2/3 | 0.666... | 66.66...% | Repeating |
| 3/4 | 0.75 | 75% | Terminating |
| 3/8 | 0.375 | 37.5% | Terminating |
| 5/8 | 0.625 | 62.5% | Terminating |
| 7/8 | 0.875 | 87.5% | Terminating |
Frequently used fractions and their exact decimal equivalents.
Frequently asked questions
How do I convert a fraction to a decimal without a calculator?
Divide the numerator by the denominator using long division. Write the numerator inside the division bracket, add a decimal point and trailing zeros as needed, and divide step by step. Each step produces one decimal digit. For example, to convert 3/4: 3 does not divide by 4, so write 0 and bring a zero to get 30. 30 ÷ 4 = 7 remainder 2. Bring a zero to get 20. 20 ÷ 4 = 5 remainder 0. The result is 0.75. Alternatively, if the denominator divides evenly into a power of 10, multiply top and bottom to reach that power - for 3/4, multiply by 25 to get 75/100 = 0.75.
What is a repeating decimal and how do I recognise one?
A repeating decimal has a block of one or more digits that cycles forever - for example, 1/3 = 0.333... and 1/7 = 0.142857142857.... You can tell a fraction will repeat when its simplified denominator has any prime factor other than 2 or 5. This calculator labels the result as "Repeating decimal" when that is the case, so you do not need to spot it manually.
How do I convert a mixed number like 1 1/2 to a decimal?
Switch to the "Mixed number" option, enter 1 in the whole-number field, 1 in the numerator, and 2 in the denominator. The calculator converts it to the improper fraction 3/2 and then divides to get 1.5. To do it by hand: multiply the whole number by the denominator (1 × 2 = 2), add the numerator (2 + 1 = 3), and divide by the denominator (3 ÷ 2 = 1.5).
Why does rounding matter for repeating decimals?
A repeating decimal such as 1/3 = 0.333... cannot be written exactly with a finite number of digits, so any rounded version (0.3, 0.33, 0.333) is an approximation. The more decimal places you keep, the smaller the error. For most practical purposes, 4 or 6 decimal places is enough, but if you are chaining several calculations together, carry more digits to avoid rounding errors accumulating.
Is 0.1 exactly equal to 1/10?
In base-10 arithmetic, yes: 1/10 = 0.1 exactly, because 10 = 2 × 5, so its only prime factors are 2 and 5. However, computers store numbers in binary (base 2), where 1/10 cannot be represented exactly - this is why floating-point languages like JavaScript sometimes show 0.1 + 0.2 = 0.30000000000000004. This calculator works in decimal for display, so the output you see is the correct mathematical result.
How do I convert the result back to a fraction?
To reverse the conversion, write the decimal over a power of 10 with as many zeros as there are decimal places, then simplify. For 0.75: write 75/100, then divide numerator and denominator by their GCD of 25 to get 3/4. For a repeating decimal like 0.333..., let x = 0.333..., then 10x = 3.333..., subtract to get 9x = 3, so x = 3/9 = 1/3.