Convert proper fractions, improper fractions, and mixed numbers to exact decimal representations. Features repeating decimal cycle detection with vinculum overlines, long division steps, and percentages.
Converting a fraction into its decimal representation involves dividing the numerator by the denominator using standard long division. Follow these steps to determine whether the result terminates or repeats:
Place numerator inside as dividend and denominator outside as divisor.
Place decimal point after dividend and append trailing zeros as required.
Observe whether the remainder reaches zero or enters an infinite recurring cycle.
If repeating, place an overline bar above the repeating cycle of numbers.
A simplified fraction produces a terminating decimal if and only if its denominator's prime factorization contains exclusively 2s, 5s, or both:
Examples: 1/4 (2² = 0.25), 3/8 (2³ = 0.375), 7/20 (2²×5 = 0.35).
If the simplified denominator contains any prime factor other than 2 or 5 (such as 3, 7, 11, 13), the decimal repeats indefinitely:
The horizontal bar above digits indicates an infinite repeating sequence.
Divide 5.000 by 8: 50 ÷ 8 = 6 (rem 2); 20 ÷ 8 = 2 (rem 4); 40 ÷ 8 = 5 (rem 0):
Divide 5.000 by 6: 50 ÷ 6 = 8 (rem 2); 20 ÷ 6 = 3 (rem 2); remainder 2 repeats forever:
Standard calculators often truncate repeating decimals with rounding errors. This converter tracks exact recurring remainders, pinpointing cycle periods and overline vinculum notations.
Machinists convert fractions like 7/32 in or 19/64 in to precision thousandths of an inch (0.2188 in, 0.2969 in) for automated CAD and CNC mills.
Displays every intermediate quotient digit and subtraction remainder, helping students learn manual arithmetic step by step.
Converts fractional basis points and mortgage interest portions (e.g. 5 3/8% = 5.375%) into usable decimal multipliers.
Generates full vertical dividend expansions with step-by-step subtraction and remainder cycles.
Formats repeating cycles with mathematical overlines (e.g. 0.\overline{142857}) and identifies the exact period length.
Handles mixed fractions seamlessly and generates exact percentage values and reciprocals instantly.
| Fraction | Decimal Value | Type | Percentage |
|---|---|---|---|
| 1 / 2 | 0.5 | Terminating | 50% |
| 1 / 3 | 0.3333... (0.3̅) | Repeating | 33.33% |
| 1 / 4 | 0.25 | Terminating | 25% |
| 1 / 5 | 0.2 | Terminating | 20% |
| 1 / 8 | 0.125 | Terminating | 12.5% |
Convert terminating and repeating decimals into fractions.
Reduce fractions to simplest form using Euclidean GCD.
Order multiple fractions ascending or descending.
Convert improper fractions to mixed numbers with remainders.
All-in-one arithmetic operations for fractions and mixed numbers.
Find the least common denominator across multiple fractions.
