โ Decimal to Fraction Converter
By Shihab Mia ยท Updated 2026-07-08
Type any terminating decimal, with or without a whole-number part.
Enter a fraction to see its decimal value and lowest terms.
To convert a decimal to a fraction, write the decimal over a power of ten based on how many digits sit after the point, then divide the top and bottom by their greatest common divisor. For example 0.75 becomes 75/100, which simplifies to 3/4. This converter does that instantly: type a decimal such as 0.75 and read off the fraction in lowest terms (3/4), plus the mixed number form for values above one. Switch to reverse mode to enter a fraction and see its decimal value. It is handy for homework, recipes, woodworking and tape measure readings, engineering drawings, and anywhere a fraction reads more clearly than a long decimal.
What is the Decimal to Fraction Converter?
A decimal and a fraction are two ways of writing the same number. A terminating decimal (one that ends, like 0.625) can always be written as a fraction whose denominator is a power of ten. The digit positions after the point tell you the denominator: one decimal place means tenths, two means hundredths, three means thousandths, and so on. So 0.625 starts life as 625/1000 before you simplify it. Reading the place value correctly is the whole trick, because 0.6, 0.06, and 0.006 are 6/10, 6/100, and 6/1000, which are very different sizes.
Simplifying, also called reducing to lowest terms, means dividing the top and bottom by their greatest common divisor (GCD). For 625/1000 the GCD is 125, so dividing both by 125 gives 5/8. The value never changes when you do this, only the way it is written, because 625 divided by 1000 and 5 divided by 8 are both exactly 0.625. This tool computes the GCD with the Euclidean algorithm and divides through automatically, so you always land on the simplest form in one step rather than reducing by hand in several passes.
When the decimal is greater than one, the same fraction can be shown as a mixed number: a whole part plus a proper fraction. For example 2.4 becomes 24/10, which reduces to 12/5, and 12/5 is the same as the mixed number 2 and 2/5. To get there you divide the numerator by the denominator: the quotient is the whole number and the remainder over the original denominator is the proper fraction. The reverse direction simply divides the numerator by the denominator, so 3/8 becomes 0.375.
Repeating decimals are a special case. A value like 0.3333... is not exactly 3333/10000; it equals 1/3 exactly. To convert a repeating decimal by hand you set it equal to x, multiply by a power of ten that shifts one full repeating block to the left of the point, subtract the original equation to cancel the endless tail, and solve. For 0.333... that gives 10x minus x equals 3, so 9x equals 3 and x equals 3/9, which is 1/3. A quick shortcut for a purely repeating decimal is to put the repeating digits over the same number of nines, so 0.4545... is 45/99, which reduces to 5/11. This converter treats the decimal you type as a terminating value, so use the algebraic method above when you need the exact fraction of a truly repeating decimal.
Whether a fraction produces a terminating or a repeating decimal depends only on its denominator in lowest terms. If the denominator has no prime factors other than 2 and 5, the decimal terminates (for example 3/8 and 7/20). If any other prime factor is present, such as 3 or 7, the decimal repeats forever (for example 1/3 and 2/7). That is why halves, quarters, eighths, and tenths convert cleanly while thirds and sevenths do not.
When to use it
- Turning a measurement like 0.375 inch into the fraction 3/8 inch for a tape measure, ruler, or socket set.
- Checking a maths homework answer by converting a decimal back into its simplest fraction.
- Scaling a recipe where 0.25 cup is easier to measure as 1/4 cup or 0.5 teaspoon as 1/2 teaspoon.
- Reading an engineering or woodworking drawing that mixes decimal and fractional dimensions.
- Converting a percentage or probability into a fraction, for example 0.2 into 1/5 for a report.
- Prepping tutoring or classroom examples that show the same value as a decimal, a fraction, and a mixed number.
How to use the Decimal to Fraction Converter
- Make sure the Decimal to fraction mode is selected.
- Type the decimal value you want to convert (for example 0.75).
- Read the fraction in lowest terms, the mixed number form, and the decimal back.
- To go the other way, click Fraction to decimal and enter a numerator and denominator.
- For a repeating decimal, use the algebraic method in the guide below to get the exact fraction.
Formula & method
Worked examples
Convert 0.625 to a fraction in lowest terms.
- 0.625 has 3 decimal places, so multiply and divide by 10 to the power 3 (1000)
- This gives 625/1000
- Find the greatest common divisor of 625 and 1000, which is 125
- Divide both by 125: 625 divided by 125 = 5 and 1000 divided by 125 = 8
Result: 0.625 = 5/8
Convert 2.4 to a fraction and a mixed number.
- 2.4 has 1 decimal place, so write it as 24/10
- The greatest common divisor of 24 and 10 is 2
- Divide both by 2: 24 divided by 2 = 12 and 10 divided by 2 = 5, giving 12/5
- 12 divided by 5 is 2 with a remainder of 2, so the mixed number is 2 and 2/5
Result: 2.4 = 12/5 = 2 2/5
Convert the repeating decimal 0.666... to its exact fraction.
- Let x = 0.666... with the 6 repeating forever
- Multiply by 10 to shift one repeating digit left: 10x = 6.666...
- Subtract the first equation from the second: 10x minus x = 6.666... minus 0.666..., so 9x = 6
- Solve: x = 6/9, then divide top and bottom by 3 to get 2/3
Result: 0.666... = 2/3 (not 666/1000)
Common decimals and their fractions in lowest terms
| Decimal | Fraction | Mixed number |
|---|---|---|
| 0.1 | 1/10 | 1/10 |
| 0.2 | 1/5 | 1/5 |
| 0.25 | 1/4 | 1/4 |
| 0.5 | 1/2 | 1/2 |
| 0.75 | 3/4 | 3/4 |
| 0.125 | 1/8 | 1/8 |
| 0.375 | 3/8 | 3/8 |
| 1.5 | 3/2 | 1 1/2 |
| 2.4 | 12/5 | 2 2/5 |
Decimal to fraction of an inch (powers of two, used on rulers and tape measures)
| Decimal (in) | Fraction (in) | Nearest |
|---|---|---|
| 0.0625 | 1/16 | sixteenth |
| 0.125 | 1/8 | eighth |
| 0.1875 | 3/16 | sixteenth |
| 0.25 | 1/4 | quarter |
| 0.3125 | 5/16 | sixteenth |
| 0.375 | 3/8 | eighth |
| 0.5 | 1/2 | half |
| 0.75 | 3/4 | quarter |
Repeating decimals and their exact fractions
| Repeating decimal | Exact fraction | Shortcut |
|---|---|---|
| 0.333... | 1/3 | 3/9 |
| 0.666... | 2/3 | 6/9 |
| 0.111... | 1/9 | 1/9 |
| 0.1666... | 1/6 | mixed repeat |
| 0.4545... | 5/11 | 45/99 |
| 0.142857... | 1/7 | 142857/999999 |
Common mistakes to avoid
- Forgetting to simplify. Writing 0.5 as 5/10 is correct but not in lowest terms. Always divide the top and bottom by their greatest common divisor, so 5/10 becomes 1/2.
- Miscounting the decimal places. The number of digits after the point sets the denominator. 0.05 has two places, so it is 5/100 (which reduces to 1/20), not 5/10.
- Treating a repeating decimal as terminating. A value like 0.3333 typed in here is treated as the terminating decimal 3333/10000, not as the exact one third. For a true repeating decimal, use the subtract-and-solve method to get the exact fraction.
- Rounding before converting. If you round 0.666 to 0.67 first, you get 67/100 instead of a value close to 2/3. Convert the most precise decimal you have, then simplify.
- Leaving an improper fraction where a mixed number is expected. For a value above one, 12/5 is a valid answer but many homework questions want the mixed number 2 and 2/5. Check which form the question asks for.
- Multiplying only the top or only the bottom. To clear the decimal you must multiply both the numerator and the denominator by the same power of ten. Multiplying just one of them changes the value.
Glossary
- Numerator
- The top number of a fraction, counting how many parts you have.
- Denominator
- The bottom number of a fraction, showing how many equal parts make a whole.
- Lowest terms
- A fraction reduced as far as possible, where the numerator and denominator share no common factor other than one.
- Greatest common divisor
- The largest whole number that divides both the numerator and denominator exactly. Dividing by it simplifies the fraction.
- Mixed number
- A whole number written together with a proper fraction, such as 2 and 2/5, for values greater than one.
- Improper fraction
- A fraction whose numerator is larger than its denominator, such as 12/5, which equals a value greater than one.
- Terminating decimal
- A decimal that ends after a finite number of digits, such as 0.625, as opposed to one that repeats forever.
- Repeating decimal
- A decimal with a digit or block of digits that repeats without end, such as 0.333..., often written with a bar over the repeating part.
Frequently asked questions
How do I convert a decimal to a fraction?
Count the digits after the decimal point. That many digits means a denominator of ten, a hundred, a thousand and so on. Write the decimal over that power of ten, then divide the top and bottom by their greatest common divisor to reach lowest terms. For example 0.75 becomes 75/100, which simplifies to 3/4.
What is 0.75 as a fraction?
0.75 is 3/4. Written over its place value it is 75/100, and dividing both numbers by 25 gives 3/4, so 0.75 equals three quarters.
What is 0.5 as a fraction?
0.5 is 1/2. It has one decimal place, so it starts as 5/10, and dividing both numbers by 5 gives 1/2.
What is 0.125 as a fraction?
0.125 is 1/8. It has three decimal places, so it is 125/1000, and dividing both numbers by their greatest common divisor of 125 gives 1/8.
What is a fraction in lowest terms?
A fraction is in lowest terms when the numerator and denominator have no common factor other than one, so it cannot be reduced further. For instance 5/8 is in lowest terms, while 50/80 is not because both can be divided by 10.
How do I write a decimal greater than one as a mixed number?
Convert it to an improper fraction first, then divide the numerator by the denominator. The quotient is the whole part and the remainder over the denominator is the fraction. So 2.4 is 12/5, and 12 divided by 5 is 2 remainder 2, giving the mixed number 2 and 2/5.
How do I convert a repeating decimal to a fraction?
Set the decimal equal to x, multiply by a power of ten that moves one repeating block to the left of the point, then subtract the original equation to cancel the endless tail and solve. For 0.666... you get 10x minus x equals 6, so 9x equals 6 and x equals 2/3. A shortcut for a purely repeating decimal is to put the repeating digits over the same number of nines, so 0.4545... is 45/99, which reduces to 5/11.
Can this tool handle repeating decimals?
It treats whatever you type as a terminating decimal. If you enter 0.3333 it returns 3333/10000, which is very close to but not exactly one third. Converting a truly repeating decimal to its exact fraction needs the algebraic subtract-and-solve method described above.
How do I convert a decimal to a fraction of an inch?
Rulers and tape measures use denominators that are powers of two, so round the decimal to the nearest 1/16, 1/32, or 1/64. For example 0.375 inch is exactly 3/8 inch, and 0.1875 inch is 3/16 inch. Multiply the decimal part by the precision you need, round to a whole number, and place it over that denominator.
How do I convert a fraction back to a decimal?
Divide the numerator by the denominator. Switch this tool to the Fraction to decimal mode and enter the two numbers, or do it by hand: 3 divided by 8 is 0.375. If the denominator has a prime factor other than 2 or 5 the result will be a repeating decimal.