Math Calculators
Fraction to Decimal Calculator
Type any fraction and get its exact decimal value, the reduced fraction, and the full long-division work, rounded to as many places as you need.
Enter whole numbers. Use a minus sign for a negative fraction.
Showing the work
To turn a fraction into a decimal, divide the top number by the bottom number. That's all the fraction bar ever means.
This calculator does that division for you with exact long division, not rounded floating-point math, so repeating decimals like 1/3 or 5/11 show their true repeating pattern instead of trailing off after a few digits.How to convert a fraction to a decimal
Every fraction is a division problem in disguise. The number above the bar (the numerator) is what's being divided; the number below the bar (the denominator) is what it's being divided by.
- Reduce first, if you can. Dividing the numerator and denominator by their greatest common factor doesn't change the value of the fraction, but it gives you smaller numbers to divide. 9/12 and 3/4 are the same fraction, and 3/4 is easier to divide by hand.
- Divide the numerator by the denominator. Set it up as long division with the numerator inside the bracket and the denominator outside, and carry the division out past the decimal point.
- Stop when the remainder hits zero, or a digit repeats. Some divisions end cleanly (terminating decimals); others fall into a repeating loop forever (repeating decimals). Either way, you now have your answer.
Worked example: 5/8
5/8 is already in lowest terms, so divide 5 by 8 directly: 5 ÷ 8 = 0.625. The division ends with no remainder, so 0.625 is exact and needs no rounding.
How to convert a fraction to a division problem?
Using a calculator makes it easy to divide numbers. If you need to do long division by hand put the top number of the fraction (numerator) inside the division bracket and the bottom number (denominator) outside, to the left of the division bracket.
The fraction 1/4 becomes 1 ÷ 4. Complete the division to convert the fraction to a decimal. It may help to simplify the fraction first to make the long division easier. For example, 9/12 = 9 ÷ 12 = 0.75. Using long division to solve this problem by hand or in your head, reducing 9/12 = 3/4, might make the problem easier. You might even know that 3/4 is equal to 0.75, because 3 quarters is equal to 75 cents.Why some fractions repeat forever
Whether a
This fraction's decimal terminates or repeats comes down to its denominator, once the fraction is fully reduced. Our number system is base ten, so a division only resolves cleanly to zero when the denominator's only prime factors are 2 and 5, the same primes that make up 10. Halves, quarters, fifths, eighths, and tenths all terminate for this reason.Bring any other prime factor into the denominator (a 3, a 7, an 11) and the division can never land on a remainder of zero. Instead the remainders start cycling, which forces the digits to cycle too. That's why 1/3 settles into 0.333... and 1/7 cycles through six digits as 0.142857142857...
Common fraction to decimal conversions
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/3 | 0.333... |
| 1/4 | 0.25 | 2/3 | 0.666... |
| 3/4 | 0.75 | 1/6 | 0.1666... |
| 1/5 | 0.2 | 5/6 | 0.8333... |
| 2/5 | 0.4 | 1/7 | 0.142857... |
| 3/5 | 0.6 | 1/9 | 0.111... |
| 4/5 | 0.8 | 1/12 | 0.08333... |
| 1/8 | 0.125 | 1/16 | 0.0625 |
Two more worked examples
20/24 → reduce, then divide
20 and 24 share a greatest common factor of 4, so 20/24 reduces to 5/6 first. Dividing 5 by 6 gives 0.8333..., a repeating decimal. Rounded to three decimal places, 5/6 ≈ 0.833.
-7/2 → handle the sign, then divide
Treat the sign separately from the division: 7 ÷ 2 = 3.5, and since exactly one of the two numbers is negative, the answer is -3.5.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. The fraction bar means "divided by," so 3/4 becomes 3 divided by 4, which equals 0.75. Reducing first doesn't change the answer, but it can make the division easier.
Why do some fractions turn into repeating decimals?
A reduced fraction only terminates when its denominator's prime factors are limited to 2s and 5s. Any other prime factor (3, 7, 11, and so on) forces the digits into a repeating cycle, like 1/3 = 0.333... or 1/7 = 0.142857142857...
How do you convert a mixed number to a decimal?
Turn it into an improper fraction first: multiply the whole number by the denominator and add the numerator. 2 1/4 becomes 9/4, and 9 ÷ 4 = 2.25.
How do you round a repeating decimal?
Look at the digit right after the place you're rounding to. Five or higher rounds the previous digit up; anything lower leaves it alone. 1/3 = 0.333... rounded to two places is 0.33.
Is a fraction the same thing as a ratio?
They use numbers the same way but mean different things: a fraction like 3/4 is a part of one whole, while a ratio like 3:4 compares two separate quantities. Both convert to decimal form the same way: divide the first number by the second.
What's the decimal form of a negative fraction?
Convert it as if both numbers were positive, then make the result negative if exactly one of the numerator or denominator was negative. -3/4 = -0.75, while -3/-4 = 0.75.