Converter Tools
Decimal Fraction Converter
Convert decimals to fractions and fractions to decimals in your browser. Handles repeating decimals like 0.(3), mixed numbers, and shows step-by-step working.
Mark a repeating block with parentheses, like 0.(3) for one third or 0.1(6) for one sixth. You can also paste 0.333... and the repeating tail will be detected.
Try a preset
Result as a fraction
3/4
Already in simplest form (no common factor between top and bottom).
Improper fraction
3/4
Mixed number
3/4
No mixed form (the value is less than 1 in magnitude).
Decimal value
0.75
Exact decimal form.
Step-by-step
- Multiply by 10^2 = 100 to clear the decimal: 75/100.
- Divide both numerator and denominator by gcd(75, 100) = 25.
How the conversion works
- Terminating decimals (like 0.75) become a fraction by writing the digits over a power of ten and dividing top and bottom by their greatest common divisor. 0.75 = 75/100 = 3/4.
- Repeating decimals (like 0.333... or 0.1666...) are solved with the standard x = (n - m) / (10^(p+r) - 10^p) trick. The result is the exact fraction, not a rounded approximation.
- Mixed numbers like 7/4 are shown both as the improper fraction and the equivalent mixed number 1 3/4. Toggle the view to copy whichever form you need.
- Going the other way, fractions divide out by long division. The tool detects whether the result terminates or repeats and shows the exact repetend (the digits inside the parentheses).
- Privacy: the numbers you type are processed in your browser. Nothing is uploaded.
How to use
- Pick the direction you need at the top: Decimal to fraction or Fraction to decimal.
- Type the value, like 0.75, 0.(3), 1.625, 3/4, 7/4, or 1 3/4. Negative numbers are accepted with a leading minus sign.
- For repeating decimals, write the repetend in parentheses (0.(3) for 0.333..., 0.1(6) for 0.1666...). The tool also detects trailing-dot forms like 0.333... automatically.
- Read the simplified fraction, the mixed-number form, and the decimal value, plus the step-by-step explanation.
- Toggle Mixed number / Improper fraction to switch how the result is displayed, or click Swap to send the result into the other input and convert the other way.
About this tool
Decimal Fraction Converter is a two-way calculator that turns any decimal into an exact fraction in lowest terms and any fraction into its full decimal expansion. The tool handles the gnarly cases that most online converters silently get wrong: repeating decimals like 0.333..., 0.1666..., and 0.142857... become exact fractions (1/3, 1/6, 1/7) using the standard geometric-series algebra rather than a rounded approximation. Mark a repeating block with parentheses (0.(3) for one third, 0.1(6) for one sixth) or paste a trailing-dot form like 0.333... and the repeating tail is detected automatically. Going the other way, every fraction is divided out by long division and the result is reported as a terminating decimal (0.75) or a repeating decimal with the exact repetend in parentheses (1/7 = 0.(142857)). Mixed numbers like 1 3/4 and improper fractions like 7/4 work in both directions, and a toggle switches between the two presentation forms so you can copy whichever your worksheet, recipe, or build plan needs. Negative values, leading zeros, and whitespace are all parsed without ceremony. The result panel shows the simplified fraction (no common factor between top and bottom), the equivalent mixed number when the value is greater than one, the decimal value, and a step-by-step breakdown that reads like a math homework explanation: clear the decimal, divide by the greatest common divisor, simplify. Useful for school homework (algebra, pre-algebra, fraction arithmetic), kitchen measurements (converting 0.625 cup to 5/8 cup), woodworking and machining (converting decimal inches to imperial fractions), engineering drawings, finance worksheets, and any time the question is `what fraction equals this decimal`. Everything runs locally in your browser, so the values you check here never leave your device.
Free to use. Works in your browser. No signup, no login.
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