Decimal to Fraction Converter
Convert any decimal to its exact fraction in simplest form — including recurring decimals like 0.333... = 1/3, 0.142857... = 1/7, and mixed recurring decimals like 0.1666... = 1/6. Shows the complete step-by-step algebraic solution, mixed number form, GCD, and percentage equivalent. Free, private, and 100% client-side. No signup required.
Enter any decimal — terminating or recurring — and get the exact fraction in simplest form. For recurring decimals, use 0.(3) for 0.333..., 0.1(6) for 0.1666..., or 0.333... for auto-detection. All calculations run locally in your browser.
Recurring notation: 0.(3) = 0.333..., 0.1(6) = 0.1666..., 0.(142857) = 0.142857...
0.(3)→ 0.333... (1/3)0.(6)→ 0.666... (2/3)0.1(6)→ 0.1666... (1/6)0.(142857)→ 0.142857142857... (1/7)0.333...→ Auto-detect recurring block1.(3)→ 1.333... (4/3)The most accurate decimal to fraction converter online — handles both terminating and recurring decimals with full step-by-step algebraic solutions.
Instant Decimal to Fraction Conversion
Convert any decimal to its exact fraction in simplest form instantly. The decimal to fraction converter shows the simplified fraction, mixed number form, GCD, decimal check, and percentage equivalent in one click.
Handles Recurring Decimals
Convert recurring (repeating) decimals like 0.333... = 1/3, 0.142857... = 1/7, and mixed recurring decimals like 0.1666... = 1/6 using the exact algebraic method. Supports parentheses notation 0.(3) and auto-detection.
Secure Decimal to Fraction Converter Online
Every conversion runs entirely in your browser using client-side JavaScript. Your inputs never leave your device — complete privacy, zero server uploads, no tracking.
100% Free — No Signup Required
The decimal to fraction converter is completely free with no account, no ads, and no usage limits. Convert as many decimals as you need, any time, on any device.
See how students, engineers, chefs, and professionals use the decimal to fraction converter in their daily work.
Math Homework & Exams
Students use the decimal to fraction converter to verify homework answers and understand the step-by-step algebraic method for converting recurring decimals. The solution breakdown shows exactly how 0.333... becomes 1/3.
Algebra & Number Theory
Mathematicians and students use the decimal to fraction converter to find exact rational representations of decimals. Converting 0.142857142857... to 1/7 reveals the underlying fraction that generates the repeating pattern.
Engineering & Technical Drawings
Engineers convert decimal measurements to fractions for technical drawings and machining specifications. Converting 0.625 inches to 5/8 inch matches standard fractional drill bit and wrench sizes.
Cooking & Recipe Scaling
Chefs and home cooks convert decimal measurements to fractions for recipe accuracy. Converting 0.75 cups to 3/4 cup or 0.333... cups to 1/3 cup matches standard measuring cup markings.
Manufacturing & Quality Control
Quality control engineers convert decimal tolerances to fractional form for inspection gauges and go/no-go fixtures. The decimal to fraction converter ensures exact fractional equivalents for imperial measurement systems.
Music Theory & Rhythm
Music theorists convert decimal beat values to fractional note durations. Converting 0.25 to 1/4 (quarter note), 0.125 to 1/8 (eighth note), or 0.333... to 1/3 (triplet) helps with rhythmic notation and time signature analysis.
A complete guide to converting terminating and recurring decimals to exact fractions using the algebraic method.
What is Decimal to Fraction Conversion?
Decimal to fraction conversion is the process of expressing a decimal number as an exact rational fraction (numerator ÷ denominator). Every terminating decimal and every recurring decimal is a rational number and can be expressed as an exact fraction. For example, 0.75 = 3/4 (terminating) and 0.333... = 1/3 (recurring). The decimal to fraction converter uses the algebraic method for recurring decimals and the power-of-10 method for terminating decimals, then simplifies using the Greatest Common Divisor (GCD).
How Our Decimal to Fraction Converter Works
- 1Enter your decimal: Type any decimal number. For recurring decimals, use parentheses notation
0.(3)or trailing dots0.333.... Or click a quick example to pre-fill. - 2Click Convert: The converter applies the correct method (power-of-10 for terminating, algebraic for recurring), simplifies using GCD, and shows the result instantly. All calculations run locally in your browser — your input never leaves your device.
- 3Read the full solution: The result shows the simplified fraction, mixed number form (if applicable), GCD, decimal check, percentage, and a complete step-by-step algebraic solution.
Methods Used for Conversion
- Terminating Decimals (Power-of-10 Method): Write the decimal as a fraction with a power of 10 as the denominator. For 0.75: 75/100, then simplify by GCD(75, 100) = 25 → 3/4.
- Pure Recurring Decimals (Algebraic Method): Let x = 0.333..., multiply by 10: 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. The denominator is always (10^n − 1) where n is the length of the recurring block.
- Mixed Recurring Decimals: For 0.1666... (non-recurring "1", recurring "6"): multiply by 10 and 100, subtract to eliminate the recurring part, giving 90x = 15, so x = 15/90 = 1/6.
- Simplification (GCD): After conversion, the fraction is simplified to its lowest terms by dividing both numerator and denominator by their Greatest Common Divisor (GCD), computed using the Euclidean algorithm.
Terminating Decimals
A decimal that ends after a finite number of digits. Examples: 0.5 = 1/2, 0.75 = 3/4, 0.125 = 1/8. All terminating decimals have denominators that are products of only 2s and 5s.
Recurring Decimals
A decimal where one or more digits repeat infinitely. Examples: 0.333... = 1/3, 0.142857142857... = 1/7. Every fraction with a denominator containing prime factors other than 2 and 5 produces a recurring decimal.
Simplest Form
A fraction is in simplest form (lowest terms) when the GCD of the numerator and denominator is 1. For example, 6/8 simplifies to 3/4 because GCD(6, 8) = 2. The decimal to fraction converter always returns the simplest form.
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A decimal to fraction converter is a tool that converts a decimal number to its exact fraction form in simplest terms. Our decimal to fraction converter handles both terminating decimals (like 0.75 = 3/4) and recurring decimals (like 0.333... = 1/3), and shows a complete step-by-step algebraic solution. It runs entirely in your browser with no signup required.
Let x = 0.333... Multiply both sides by 10: 10x = 3.333... Subtract the original equation: 10x − x = 3.333... − 0.333..., so 9x = 3, giving x = 3/9 = 1/3. Enter "0.(3)" or "0.333..." in the decimal to fraction converter above to see this solution automatically.
0.75 has two decimal places, so write it as 75/100. Find the GCD of 75 and 100: GCD(75, 100) = 25. Divide both by 25: 75 ÷ 25 = 3, 100 ÷ 25 = 4. So 0.75 = 3/4. The decimal to fraction converter performs this automatically for any terminating decimal.
0.1666... has a non-recurring part "1" and a recurring block "6". Let x = 0.1666... Multiply by 10: 10x = 1.666... Multiply by 100: 100x = 16.666... Subtract: 90x = 15, so x = 15/90 = 1/6. Enter "0.1(6)" in the decimal to fraction converter to see this solution.
A terminating decimal ends after a finite number of digits (e.g. 0.5, 0.75, 0.125). A recurring decimal has one or more digits that repeat infinitely (e.g. 0.333..., 0.142857142857...). Both types are rational numbers and can be expressed as exact fractions. Non-recurring, non-terminating decimals (like π = 3.14159...) are irrational and cannot be expressed as fractions.
Use parentheses notation to mark the recurring block: 0.(3) for 0.333..., 0.1(6) for 0.1666..., 0.(142857) for 0.142857142857... You can also type "0.333..." with trailing dots and the converter will auto-detect the recurring block. Click any of the quick example buttons to see the notation in action.
The algebraic method uses multiplication and subtraction to eliminate the recurring part. For a pure recurring decimal with n repeating digits, multiply by 10^n and subtract the original equation. The recurring part cancels out, leaving a simple equation to solve. For mixed recurring decimals, two multiplications are needed to isolate the recurring block.
Yes, completely. All conversions are performed locally in your web browser using client-side JavaScript. No inputs, results, or steps are ever sent to any server. Your data stays entirely on your device.
Yes. The decimal to fraction converter is 100% free with no account registration, no payment, and no usage limits. Convert as many decimals as you need, any time, on any device.