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Decimal to Fraction Calculator
Convert decimals into simplified fractions, mixed numbers, improper fractions, and repeating decimal fractions with clear step by step work.
Convert decimal to fraction
Enter a decimal like 0.75, 1.625, -2.5, or 0.333.
Step by step work
Quick examples
How to use this decimal to fraction calculator
Enter your decimal
Type a decimal number such as 0.125, 0.75, 1.625, or -2.5.
Choose repeating digits
Select how many final digits repeat, or leave it as none for a standard decimal.
Click convert
The calculator shows the simplified fraction, mixed number, and GCD.
Check the steps
Read the calculation steps to understand how the fraction was reduced.
What is decimal to fraction conversion?
Decimal to fraction conversion changes a decimal number into a ratio of two whole numbers. For example, 0.75 becomes 75/100, which reduces to 3/4. The two forms represent exactly the same value, just written differently.
Fractions are useful when you need exact values for math, measurements, recipes, construction, schoolwork, and algebra, since decimals are sometimes rounded while a simplified fraction can represent a value exactly.
Decimal to fraction formula
For a terminating decimal, count the digits after the decimal point. Put the number without the decimal point over 10, 100, 1000, or another matching power of 10, then simplify by dividing both numbers by their greatest common divisor.
Repeating decimal to fraction
A repeating decimal has one or more digits that continue forever. For example, 0.666... equals 2/3, and 0.363636... equals 4/11. Use the repeating digits option above when the final digits of your decimal repeat in a clear pattern.
If you would rather see how a decimal behaves in binary rather than as a fraction, the Decimal to Binary Converter shows the same kind of place value breakdown, just using base 2 instead of base 10.
Common decimal to fraction table
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.5 | 1/2 |
| 0.625 | 5/8 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
| 1.25 | 1 1/4 |
| 2.5 | 2 1/2 |
Where this fits with other math tools
Fractions and decimals show up together in a lot of everyday math, so this calculator pairs naturally with a few other tools. If a fraction result also matters as a percentage, for example turning 3/4 into 75 percent, the Percentage Calculator can handle that conversion directly. If you are working with a long or rounded decimal and want to control precision before converting it, the Significant Figures Calculator can help you round consistently first.
Square roots are a common source of decimals that never terminate or repeat, since most are irrational. The Square Root Calculator can show you a decimal approximation alongside the simplified radical form, which is a useful companion when a decimal from this calculator turns out not to convert to a clean fraction at all.
Frequently asked questions
What is a decimal to fraction calculator?
A decimal to fraction calculator converts a decimal number, such as 0.75, into a simplified fraction, such as 3/4. It works for whole numbers with a decimal part, negative decimals, and repeating decimals when you specify which digits repeat.
How do you convert a decimal to a fraction?
Write the decimal over 1, then multiply the numerator and denominator by a power of 10 to remove the decimal places. Finally, reduce the fraction by dividing both numbers by their greatest common divisor until it cannot be simplified further.
What is 0.75 as a fraction?
0.75 as a fraction is 3/4. It starts as 75/100, and since both numbers share a greatest common divisor of 25, dividing both by 25 gives the simplified fraction 3/4.
Can this calculator convert repeating decimals?
Yes. Enter the decimal and choose how many final digits repeat. For example, enter 0.6 and choose 1 repeating digit to get 2/3, or enter 0.36 and choose 2 repeating digits to get 4/11.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator larger than the denominator, such as 13/8. A mixed number expresses the same value with a whole number and a fraction, such as 1 5/8. Both represent the exact same quantity.
Why does the calculator show the greatest common divisor?
The greatest common divisor, or GCD, is the largest number that divides both the numerator and denominator evenly. Showing it helps confirm that a fraction has been fully reduced, since dividing by anything smaller would leave it unsimplified.
Does every decimal convert to an exact fraction?
Every terminating decimal converts to an exact fraction, and every repeating decimal with a clearly defined repeating pattern also converts to an exact fraction. Non repeating, non terminating decimals, such as pi, cannot be written as an exact fraction of whole numbers.
This tool is for educational purposes only. Always verify important results with a qualified professional.
