Decimal to Fraction Calculator
Convert any decimal number to a simplified fraction in lowest terms, with step-by-step working. Handles terminating and long decimals.
Did this tool work for you?
How to use this calculator
Write the decimal as a fraction with denominator 10^n (where n = number of decimal places), then simplify using the Greatest Common Divisor.
- 1
Enter the decimal number you want to convert.
- 2
The fraction in lowest terms is shown with a three-step explanation.
- 3
If the fraction is improper (numerator > denominator), the mixed number is also displayed.
- 4
The decimal verification confirms the fraction equals your original input.
Frequently asked questions
How do you convert a decimal to a fraction manually?
Write the decimal over 1 (e.g., 0.625/1). Multiply numerator and denominator by 10 for each decimal place (0.625 has 3 places → multiply by 1000: 625/1000). Find the GCD of 625 and 1000: GCD = 125. Divide both by 125: 5/8. So 0.625 = 5/8.
What if my decimal has many places?
The same method works but the intermediate fraction has a large denominator before simplification. For 0.142857 (≈ 1/7): 142857/1000000; GCD = 142857, giving 1/7. This calculator handles up to about 8–10 significant decimal places before floating-point precision becomes a factor.
Can repeating decimals be converted exactly?
Repeating decimals (like 0.333…) require a different algebraic approach: let x = 0.333…; 10x = 3.333…; 10x − x = 3; 9x = 3; x = 1/3. This calculator works with the finite decimal you enter — for repeating decimals, enter a sufficient number of digits and the result will closely approximate the exact fraction.
What is a mixed number?
A mixed number combines a whole number and a proper fraction: 1¾ instead of 7/4. It is easier to interpret for quantities greater than 1 — "one and three-quarters cups" is clearer than "seven-quarter cups." Improper fractions (numerator > denominator) can always be rewritten as mixed numbers.
Decimal to fraction — simplify with GCD and show mixed number
The GCD method explained
The key to decimal-to-fraction conversion is the GCD (Greatest Common Divisor). After writing the decimal as a ratio (e.g., 625/1000), the GCD of numerator and denominator tells us the largest factor that divides both — dividing by it gives the simplest form. The Euclidean algorithm finds the GCD efficiently: GCD(625, 1000) = GCD(625, 375) = GCD(375, 250) = GCD(250, 125) = GCD(125, 0) = 125. So 625/1000 = 5/8.
Terminating vs. repeating: which decimals are fractions?
Every terminating decimal is a fraction (rational number). Repeating decimals are also rational — 0.142857142857… = 1/7. Non-terminating, non-repeating decimals (like π = 3.14159… or √2 = 1.41421…) are irrational numbers and cannot be expressed as fractions. If a decimal terminates or repeats, it is guaranteed to have a fractional equivalent.
When fractions are more useful than decimals
Fractions preserve exactness in arithmetic. 1/3 + 1/6 = 1/2 exactly; as decimals: 0.3333… + 0.1666… = 0.5 (requires rounding). In baking and carpentry, fractions (3/4 cup, 5/8 inch) are the standard — not because of tradition but because rulers and measuring cups are divided into halves, quarters, and eighths. Fractions also reveal relationships: 0.333… is just "a number," but 1/3 shows it is exactly one part of three equal parts.
Learn more from an authoritative source:
WikipediaScientific Calculator
Evaluate mathematical expressions including trigonometry, logarithms, exponents, and more.
Percentage Calculator
Quickly calculate percentages, percentage change, and percentage of a total.
Fraction Calculator
Add, subtract, multiply, or divide two fractions and get the simplified result instantly.
Ratio Calculator
Simplify ratios, find missing values, and scale ratios up or down.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →