Decimal to Fraction Calculator
Decimal to convert
Type any decimal, such as 0.75, 2.375 or 0.125.
Up to 12 digits after the point convert exactly.
Simplified fraction
awaiting inputAwaiting input.
Enter a decimal to convert.
- Mixed number
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- Improper fraction
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- Unreduced fraction
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- Percentage
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To convert a decimal to a fraction, write the digits after the decimal point over a power of 10 matching their count, then simplify by dividing both numbers by their greatest common divisor. 0.75 becomes 75/100, and dividing both by their GCD of 25 gives the simplified answer, 3/4.
What a Fraction Actually Is
A fraction represents a part of a whole as two integers: a numerator on top counting how many parts you have, and a denominator on the bottom counting how many equal parts the whole was divided into.
In 3/4, the denominator 4 says the whole was cut into four equal pieces, and the numerator 3 says you have three of them. A decimal expresses the same value using place value instead — tenths, hundredths, thousandths — so 0.75 and 3/4 are two notations for the identical quantity, exactly the way 5 3/8 in and 5.375 in describe the same length in the imperial system.
Converting between the two notations matters because different contexts favour different ones. Recipes, carpentry and tool sizes are usually given as fractions because that is what a measuring cup or a ruler graduates in. Calculators, spreadsheets and most scientific work default to decimals because they are easier to add, multiply and compare directly.
The Decimal to Fraction Formula
Four variables carry a decimal to its simplified fraction. Each is defined below, then applied to a worked conversion.
K is how many digits follow the decimal point. N is those digits read as a whole number. P is 10 raised to the power of K. G is the greatest common divisor of N and P, which reduces N/P to lowest terms.
- DThe input decimal — the value you want to convert, such as 0.75.
- KThe count of digits after the decimal point. 0.75 has K = 2.
- NThe numerator before simplifying — the decimal digits read as an integer. For 0.75, N = 75.
- PThe denominator before simplifying — 10 raised to the power K. For K = 2, P = 100.
- GThe greatest common divisor of N and P, used to reduce the fraction.
Worked calculation — D = 0.75
- K = 2Two digits follow the decimal point
- N = 75, P = 100Read the digits as an integer over 10²
- G = GCD(75, 100) = 25The largest number dividing both evenly
- 75 ÷ 25 = 3, 100 ÷ 25 = 4Divide both by G
0.75 = 75/100 = 3/4
This method only works directly on terminating decimals — ones with a finite number of digits. A repeating decimal such as 0.333… has infinitely many digits, so K is undefined and the place-value method cannot be applied; it needs the algebraic method covered in the FAQ below instead.
Proper, Improper and Mixed
Every fraction falls into one of these categories, and knowing which one you are looking at tells you immediately whether the value is less than, equal to, or greater than one.
Proper fraction
The numerator is smaller than the denominator, such as 3/4 or 5/8. A proper fraction always represents a value between 0 and 1.
Improper fraction
The numerator is equal to or greater than the denominator, such as 9/4. An improper fraction represents a value of 1 or more and can be rewritten as a mixed number.
Mixed number
A whole number and a proper fraction written together, such as 2 1/4 — the same value as the improper fraction 9/4, just split into its whole and fractional parts.
Converting between improper and mixed forms is division with a remainder: 9/4 means 9 ÷ 4, which is 2 remainder 1, so the whole part is 2 and the leftover 1 stays over the original denominator — 2 1/4. Reversing it multiplies the whole number by the denominator and adds the numerator: 2 1/4 becomes (2 × 4) + 1 = 9 over 4, or 9/4. The mixed number calculator runs both directions for you.
Common Decimal to Fraction Values
The decimals that come up constantly in cooking, crafts and everyday maths, already simplified.
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.3 | 3/10 |
| 0.333… | 1/3 |
| 0.4 | 2/5 |
| 0.5 | 1/2 |
| 0.6 | 3/5 |
| 0.625 | 5/8 |
| 0.666… | 2/3 |
| 0.7 | 7/10 |
| 0.75 | 3/4 |
| 0.8 | 4/5 |
| 0.875 | 7/8 |
| 0.9 | 9/10 |
Converting Without a Calculator
The same three steps work for any terminating decimal, and most people can do them mentally for anything up to three decimal places.
- Count the decimal places. 0.125 has three digits after the point.
- Write the digits over 1 followed by that many zeros. 0.125 becomes 125/1000.
- Divide both numbers by their greatest common divisor. The GCD of 125 and 1000 is 125, giving 1/8.
Finding the GCD by hand is usually fastest by repeatedly dividing out small factors — 2, then 5, then 5 again — rather than searching for the full number at once. If you divide by a factor and one side stops dividing evenly, back up and try the next prime instead.
Frequently Asked Questions
What is 0.75 as a fraction?
0.75 as a fraction is 3/4. Multiply 0.75 by 100 to get 75/100, then divide both the numerator and denominator by their greatest common divisor of 25 to reach 3/4 in lowest terms.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD) — the largest number that divides both evenly. For 8/12, the GCD of 8 and 12 is 4, so dividing both by 4 gives 2/3, which cannot be reduced further.
What is a proper vs improper fraction?
A proper fraction has a numerator smaller than its denominator, such as 3/4, and its value is always less than 1. An improper fraction has a numerator equal to or greater than its denominator, such as 5/4, and its value is 1 or more. An improper fraction can always be rewritten as a mixed number.
Can every decimal become a fraction?
Every terminating decimal, like 0.75, converts directly to an exact fraction using its place value. Every repeating decimal, like 0.333…, also has an exact fraction — 1/3 in this case — found with the algebraic subtraction method rather than place value. Only an irrational number such as π has no fraction at all, because its digits never terminate or settle into a repeating pattern.
What is a repeating decimal as a fraction?
A repeating decimal converts to a fraction by algebra rather than place value. For 0.333…, let x = 0.333…, so 10x = 3.333…. Subtracting the first equation from the second gives 9x = 3, so x = 3/9, which simplifies to 1/3. The same method turns 0.1666… into 1/6 and 0.181818… into 2/11.
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