Converting a decimal to a fraction means expressing the same numerical value as a ratio of two integers and reducing that ratio to lowest terms. This converter supports terminating decimals and explicit repeating-decimal notation.
How to Convert a Terminating Decimal to a Fraction
For a terminating decimal, count the digits after the decimal point. Remove the decimal point to create the numerator, then use a power of 10 as the denominator.
where n is the number of decimal places.
Example: Convert 0.875 to a Fraction
0.875 has 3 decimal places.
Initial fraction: 875/1000
GCD of 875 and 1000 = 125
875 ÷ 125 = 7
1000 ÷ 125 = 8
Result: 7/8
Repeating Decimal to Fraction
A repeating decimal continues forever in a repeating pattern. In this calculator, place only the repeating digits inside parentheses.
Examples of supported repeating notation:
0.(3) = 0.333…
0.(36) = 0.363636…
1.8(3) = 1.8333…
Example: Convert 0.(3) to a Fraction
Let x = 0.333…
10x = 3.333…
10x − x = 3
9x = 3
x = 3/9
x = 1/3
Decimals Greater Than 1 and Mixed Numbers
A decimal greater than 1 usually converts to an improper fraction. The same value can also be shown as a mixed number.
2.75 = 275/100
275/100 = 11/4
Improper fraction: 11/4
Mixed number: 2 3/4
Negative Decimals
A negative decimal keeps its negative sign after conversion.
Common Decimal-to-Fraction Conversions
| Decimal | Simplified Fraction |
|---|---|
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.375 | 3/8 |
| 0.5 | 1/2 |
| 0.625 | 5/8 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
| 1.5 | 3/2 = 1 1/2 |
| 2.75 | 11/4 = 2 3/4 |
Common Decimal-to-Fraction Mistakes
1. Treating a finite approximation as repeating
0.333333 is a terminating decimal input. Use 0.(3) when you mean 0.333… repeating forever.
2. Forgetting to simplify
75/100 is equivalent to 3/4, but 3/4 is the fraction in lowest terms.
3. Using the wrong denominator
Three decimal places use a denominator of 1000, not 100.
4. Losing the negative sign
-0.75 converts to -3/4.
How to Verify the Fraction
Divide the simplified numerator by the denominator. The result should reproduce the original terminating decimal or its repeating pattern. For example, 7 ÷ 8 = 0.875.
Related Calculators
- Fraction to Decimal Converter — convert a fraction back to decimal.
- Ratio Calculator — compare values as a ratio.
- Percentage Calculator — work with percentages and decimal relationships.
- Proportion Calculator
- Basic Math Calculators
How This Decimal to Fraction Converter Works
Terminating decimal input is processed as text rather than converted through binary floating-point arithmetic. The digits are converted into an exact numerator and a power-of-10 denominator, then reduced by their greatest common divisor.
Explicit repeating notation is converted algebraically by separating the non-repeating and repeating parts and constructing the exact rational fraction before simplification.
Prepared by the Utilixea Editorial Team.
Last updated: July 21, 2026.
Decimal to Fraction FAQs
For a terminating decimal, remove the decimal point, place the digits over a power of 10 based on the number of decimal places, then reduce the fraction by its greatest common divisor.
0.5 = 5/10, which simplifies to 1/2.
0.75 = 75/100, and dividing both numbers by 25 gives 3/4.
Yes. Enter repeating digits inside parentheses, such as 0.(3), 0.(36), or 1.8(3).
Yes. The negative sign is preserved, so -0.625 simplifies to -5/8.
The decimal converts to an improper fraction and can also be written as a mixed number. For example, 2.75 = 11/4 = 2 3/4.
A mixed number combines a whole number with a proper fraction, such as 2 3/4.
Simplifying expresses the same value in lowest terms, where the numerator and denominator have no common factor greater than 1.
Need the reverse conversion? Use the Fraction to Decimal Converter or explore Basic Math Calculators.
