Decimal to Fraction Calculator — Simplified & Mixed Numbers
Type any decimal — positive, negative or mixed — and get the fully simplified fraction and mixed number equivalent, with the numerator, denominator and the GCD simplification step.
3/4
- 1
Count decimal places
n = 2 = 2 - 2
Scale to integer
0.75 × 100 = 75Multiplying by 10ⁿ clears the decimal point; denominator is also 100. - 3
Divide by GCD
GCD(75, 100) = 25 = 3 / 4 - 4
Simplified fraction
3 ÷ 4 = 0.75000000
How does this calculator work?
Multiply the decimal by 10^(decimal-places) to get an integer numerator and denominator, then divide both by their GCD to simplify. Example: 0.75 → 75/100 ÷ GCD(75,100)=25 → 3/4. For values above 1, the mixed-number form is also shown (e.g. 1.75 = 7/4 = 1 and 3/4).
Formula
How this is calculated
To convert a terminating decimal to a fraction, count the number of decimal places (n), multiply the decimal by 10^n to get a whole number, then place that over 10^n as the denominator. For 0.75: multiply by 100 to get 75/100. Then find the greatest common divisor (GCD) of numerator and denominator using the Euclidean algorithm (75 and 100 share a GCD of 25), and divide both by it: 75/100 = 3/4.
For numbers greater than 1, the simplified fraction can also be written as a mixed number: the whole part is the integer quotient and the remainder becomes the new numerator. For 1.75 = 7/4, the mixed form is 1 and 3/4.
This calculator handles up to 8 decimal places of precision. Repeating (recurring) decimals such as 0.333… require a different algebraic method (multiply by 10 and subtract) and are not covered here — the result for 0.333333 will be 333333/1000000 rather than 1/3 because the input is a finite approximation. For exact repeating decimals use the fraction calculator or enter the known fraction directly.
Frequently asked questions
0.125 has 3 decimal places, so it starts as 125/1000. The GCD of 125 and 1000 is 125, giving 1/8.
Let x = 0.333…, then 10x = 3.333… Subtract: 9x = 3, so x = 1/3. This algebraic method is not handled by this calculator — enter 0.333333 and you get a close approximation, not the exact 1/3.
A mixed number combines a whole part and a proper fraction: 7/4 = 1 and 3/4. It is easier to read for quantities greater than 1 (e.g. 1¾ cups of flour) but the improper fraction form (7/4) is easier for arithmetic.
Also known as
TG we-Calculate Editorial Team. (2026). Decimal to Fraction Calculator — Simplified & Mixed Numbers [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/decimal-to-fraction-calculator
TG we-Calculate Editorial Team. "Decimal to Fraction Calculator — Simplified & Mixed Numbers." TG we-Calculate. 2026. https://we-calculate.com/calculator/decimal-to-fraction-calculator.
TG we-Calculate Editorial Team, "Decimal to Fraction Calculator — Simplified & Mixed Numbers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/decimal-to-fraction-calculator
@misc{wecalculate_decimal_to_fraction_calculator, title = {Decimal to Fraction Calculator — Simplified & Mixed Numbers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/decimal-to-fraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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