Convert decimals to fractions and back
Last reviewed: January 2026
The Decimal to Fraction Converter is a free browser-based tool that performs this calculation instantly with no signup or downloads required. Enter your values, click calculate, and get accurate results immediately. All processing happens in your browser — nothing is sent to a server.
To convert a decimal to a fraction: write the decimal over 1, multiply both by 10 for each decimal place, then simplify by dividing by the GCD. For example, 0.75 = 75/100 = 3/4 (GCD of 75 and 100 is 25). Terminating decimals (like 0.75) convert perfectly to fractions. Repeating decimals (like 0.333…) equal exact fractions (1/3). Common conversions: 0.1=1/10, 0.125=1/8, 0.2=1/5, 0.25=1/4, 0.333…=1/3, 0.5=1/2, 0.666…=2/3, 0.75=3/4.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333... | 33.3% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.666... | 66.7% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
Decimals and fractions are two different ways of expressing the same mathematical concept — parts of a whole. Every fraction can be converted to a decimal by dividing the numerator by the denominator, and every terminating or repeating decimal can be converted to a fraction. The decimal 0.75 equals the fraction 3/4, and both represent three parts out of four equal divisions. Understanding how to convert between these representations is essential for arithmetic, measurement, cooking, construction, finance, and scientific calculations, where different contexts favor different notation.
Fractions have certain advantages: they express exact values that decimals sometimes cannot (1/3 = 0.333... repeating), they are natural for division and ratio problems, and they are standard notation in cooking, construction, and music. Decimals have their own strengths: they align with our base-10 number system, they are easier to compare (is 7/16 or 3/7 larger? — converting to 0.4375 and 0.4286 makes the comparison instant), they are required for calculator and computer input, and they connect directly to percentage notation (0.75 = 75%). Neither representation is inherently superior — mathematical fluency means being comfortable with both and knowing when each is more appropriate.
The direct method for converting a fraction to a decimal is long division — divide the numerator by the denominator. For 3/8: 3 ÷ 8 = 0.375. For common fractions, memorizing key equivalents speeds up calculations: 1/2 = 0.5, 1/3 ≈ 0.333, 1/4 = 0.25, 1/5 = 0.2, 1/6 ≈ 0.167, 1/8 = 0.125, 1/10 = 0.1, and 1/16 = 0.0625. From these base conversions, any multiple can be calculated: 3/8 = 3 × (1/8) = 3 × 0.125 = 0.375.
An alternative method uses equivalent fractions with denominators that are powers of 10. If you can convert the denominator to 10, 100, or 1000 by multiplying by an appropriate factor, the conversion becomes trivial. For 3/4: multiply both numerator and denominator by 25 to get 75/100 = 0.75. For 7/8: multiply by 125 to get 875/1000 = 0.875. This method works cleanly when the denominator's only prime factors are 2 and 5 (since 10 = 2 × 5). When the denominator contains other prime factors (3, 7, 11, etc.), the decimal representation will be repeating rather than terminating.
Converting terminating decimals to fractions follows a simple algorithm. Write the decimal digits as the numerator and the appropriate power of 10 as the denominator: 0.375 = 375/1000. Then simplify by dividing both by their greatest common factor: 375/1000 = 375÷125 / 1000÷125 = 3/8. Finding the GCF can be done through prime factorization or Euclid's algorithm. For mixed numbers, convert the fractional part separately: 2.375 = 2 + 375/1000 = 2 + 3/8 = 2 3/8 = 19/8.
Repeating decimals require a different algebraic approach. To convert 0.333... to a fraction, let x = 0.333..., multiply by 10: 10x = 3.333..., subtract: 10x - x = 3, so 9x = 3, and x = 3/9 = 1/3. For more complex repeating patterns like 0.142857142857... (which equals 1/7), let x = 0.142857142857..., multiply by 10⁶: 1,000,000x = 142857.142857..., subtract: 999,999x = 142857, and x = 142857/999999 = 1/7. This algebraic method works for any repeating decimal, though the numbers involved can become large for long repeating periods. Our Cross Multiplication Calculator helps with the fraction arithmetic that often follows conversion.
The Imperial measurement system used in the United States relies heavily on fractions — rulers are marked in halves, quarters, eighths, and sixteenths of an inch, and construction lumber is specified in fractional dimensions (a "two-by-four" is actually 1 1/2 × 3 1/2 inches). Plumbing pipe sizes use fractions (1/2", 3/4", 1 1/4"), as do drill bit sizes and wrench sizes. In cooking, recipes specify ingredients in fractions of cups, teaspoons, and tablespoons. Stock market prices were historically quoted in fractions (each fraction being 1/8 or 1/16 of a dollar) until decimalization in 2001.
The metric system, by contrast, uses decimals exclusively — 2.54 centimeters rather than 2 and 27/50 centimeters. This makes metric calculations simpler because addition, subtraction, and comparison of decimals follow straightforward place-value rules. Converting between Imperial fractional measurements and metric decimal measurements requires combining both skills — knowing that 3/4 inch equals 0.75 inches equals 19.05 millimeters requires both fraction-to-decimal conversion and unit conversion.
Several common errors occur in decimal-fraction conversions. Failing to fully simplify fractions leads to unwieldy results — 375/1000 is correct but 3/8 is far more useful. Misidentifying repeating versus terminating decimals causes problems — 0.1666... is 1/6, not 0.17 (which would be 17/100). Rounding repeating decimals before converting introduces error — converting 0.333 to a fraction gives 333/1000, not the correct 1/3. When adding fractions with unlike denominators, finding the least common denominator (LCD) before adding prevents errors — 1/3 + 1/4 requires converting to 4/12 + 3/12 = 7/12, not incorrectly adding numerators and denominators to get 2/7. For related calculations, see our Percent Error Calculator and Scientific Notation Calculator.
Computers store numbers in binary (base-2), which creates interesting challenges for decimal-fraction conversion. Many simple decimal fractions cannot be represented exactly in binary floating-point — 0.1 in decimal becomes 0.00011001100110011... in binary, an infinite repeating pattern. This is why floating-point arithmetic in programming languages sometimes produces surprising results like 0.1 + 0.2 = 0.30000000000000004. Financial software typically uses fixed-point decimal representations or integer arithmetic with cents to avoid these rounding errors. The IEEE 754 standard defines how floating-point numbers are stored in computers, using a sign bit, exponent, and mantissa to represent a wide range of values with limited precision — single precision (32-bit) provides approximately 7 significant digits of accuracy, while double precision (64-bit) provides approximately 15-16 significant digits.
Some decimals terminate (0.25 = ¼), but many common fractions produce repeating decimals: ⅓ = 0.333..., ⅙ = 0.1666..., 1/7 = 0.142857142857... The repeating block in 1/7 cycles every 6 digits. To convert a repeating decimal to a fraction, use algebra: if x = 0.333..., then 10x = 3.333..., subtract to get 9x = 3, so x = 3/9 = 1/3. Understanding this conversion is essential for avoiding rounding errors in engineering and financial calculations, where small inaccuracies compound over many operations. Calculator displays that show 0.3333333 are approximations — the exact value is always the fraction. Practice operations with both formats using our Fraction Calculator.
See also: Mixed Number Calculator · Fraction Calculator · Percentage Calculator · Ratio Calculator
→ Common decimals to know by heart. 0.25 = 1/4, 0.333... = 1/3, 0.5 = 1/2, 0.625 = 5/8, 0.75 = 3/4, 0.125 = 1/8. These come up constantly in cooking, woodworking, and everyday math. Memorizing them saves time.
→ Repeating decimals always have fraction equivalents. 0.111... = 1/9, 0.142857... = 1/7, 0.090909... = 1/11. Every repeating decimal is a rational number expressible as a fraction. The pattern length relates to the denominator — 1/7 has a 6-digit repeating cycle.
→ Irrational numbers cannot be expressed as fractions. π, √2, and e have non-repeating, non-terminating decimals. No fraction exactly equals π — 22/7 (3.142857...) and 355/113 (3.1415929...) are famous approximations. Our Fraction Calculator handles fraction arithmetic.
→ Construction measurements use fractions of inches. US construction works in 1/16" increments. 0.3125" = 5/16", 0.4375" = 7/16". When converting metric plans to imperial, this converter paired with our CM to Inches Converter handles the translation.
See also: Fraction Calculator · Mixed Number Calculator · Percentage Calculator · CM to Inches