Fraction to Decimal Calculator
Convert any fraction or mixed number to decimal form. Formula: decimal = numerator ÷ denominator. For mixed numbers, add the whole number portion.
Reviewed & updated for 2026 · How we calculate
Common fractions to decimals
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... (repeating) | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666... (repeating) | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/16 | 0.0625 | 6.25% |
| 2/3 | 0.6666... (repeating) | 66.67% |
The division algorithm behind every fraction-to-decimal conversion
Converting a fraction to a decimal is just long division. To convert 3/8, divide 3 by 8. Since 3 is less than 8, the integer quotient is 0. Add a decimal point and a zero: 30 ÷ 8 = 3 remainder 6. Add another zero: 60 ÷ 8 = 7 remainder 4. Continue: 40 ÷ 8 = 5 remainder 0. The remainder of 0 means we've terminated: 3/8 = 0.375 exactly.
When the denominator (in lowest terms) contains any prime factor other than 2 or 5, the long division never produces a remainder of zero, it cycles through a finite set of remainders, producing a repeating decimal. For 1/7, the cycle is 1 → 3 → 2 → 6 → 4 → 5 → 1 (six distinct remainders before repeating), giving 1/7 = 0.142857 142857 142857... with a six-digit repeating block.
The length of the repeating block (the "period") equals the smallest positive integer k such that 10^k ≡ 1 (mod denominator). For 1/3: 10 ≡ 1 (mod 3) so period is 1. For 1/7: period is 6. For 1/13: period is 6. For 1/17: period is 16. The mathematics of these cycles connect to number theory and have applications in cryptography, hash functions, and pseudorandom number generation.
When precision matters: significant figures and rounding
Most calculators store decimals with 15-17 significant digits (IEEE 754 double precision). A fraction like 1/3 becomes 0.3333333333333333, already an approximation, accurate to about 16 places. Most everyday math doesn't need this precision; 2-4 decimal places suffices. Scientific work might use 5-7; engineering precision is typically 3-6; financial calculations use 2 (cents). Computing with carried-forward rounding error can accumulate problems when you do millions of operations.
Practical rules: (1) For final reporting, use the number of significant digits warranted by your input precision. (2) For intermediate calculations, keep more digits than you need to avoid round-off error. (3) When summing many small numbers, the order matters, summing small first preserves precision better than summing large first. (4) For exact computation with rationals, use fraction form throughout and only convert to decimal at the end.
Where this conversion matters in real life
- Cooking and recipe scaling: A recipe calling for 2 1/3 cups translates to 2.333... cups for a digital scale. Scaling a recipe to 1.5x: 2.333 × 1.5 = 3.5 cups = 3 1/2 cups.
- Construction and machining: Imperial drawings use fractions like 3/8" or 11/16". CNC machines and digital calipers display decimals. Conversions are constant: 7/16" = 0.4375", 11/64" = 0.171875".
- Probability and statistics: Odds expressed as fractions (3:1, 5:2) convert to probabilities as decimals (0.75, 0.714). Sports betting and game theory live in this conversion space.
- Music intervals: A perfect fifth is the ratio 3:2 = 1.5x frequency. An octave is 2:1 = 2.0x. Just intonation uses these exact fractions; equal temperament approximates with irrational decimals (12th root of 2 ≈ 1.0595).
- Financial percentages: Interest rates "7 3/4%" appear in older mortgage documents, that's 7.75%. APR/APY formulas operate on the decimal form, not the fraction.
- Calibration and scientific reporting: A meter that reads "0.6875" should be understood as exactly 11/16 in fractional terms if it's measuring something with whole-number relationships.
FAQs
How do you convert a fraction to a decimal?
Divide the numerator (top) by the denominator (bottom). Example: 3/4 = 3 ÷ 4 = 0.75. For mixed numbers like 2 1/2: convert the fraction first (1/2 = 0.5), then add the whole number (2 + 0.5 = 2.5).
What is 1/3 as a decimal?
1/3 = 0.3333... (repeating). Often rounded to 0.333 or expressed as 0.3̄ (with a line over the 3). To convert: 1 ÷ 3 = 0.333...
What is 5/8 as a decimal?
5/8 = 5 ÷ 8 = 0.625. This is a 'terminating' decimal, it has a finite number of digits, unlike 1/3 which repeats.
Why do some fractions repeat as decimals?
A fraction terminates as a decimal IF the denominator (in lowest terms) only has prime factors of 2 and 5. Examples: 1/2, 1/4, 1/5, 1/8, 1/10, 1/20 all terminate. Fractions with denominators containing other primes (like 3 or 7) produce repeating decimals: 1/3, 1/6, 1/7, 1/9.
How precise is the decimal conversion?
Computer arithmetic uses double-precision floats, about 15-17 significant decimal digits of accuracy. For most everyday math, this is more precision than you need. For exact rational arithmetic (no rounding), use fraction form.