Sprint 8 Converter + Math
Fraction to Decimal Converter
Convert numerator/denominator.
Decimal
5.000000
How it works
Converting between fractions and decimals is a core arithmetic skill with practical applications in cooking measurement, engineering tolerances, financial calculations, and carpentry. The Fraction to Decimal Converter handles proper fractions, improper fractions, and mixed numbers — and shows whether the decimal result is terminating or repeating.
**Why some fractions produce repeating decimals** A fraction p/q (in lowest terms) produces a terminating decimal if and only if q has no prime factors other than 2 and 5 (i.e., q = 2ᵃ × 5ᵇ). Any other denominator produces a repeating decimal. 1/3 = 0.333... (repeating because 3 is a prime factor of denominator). 1/8 = 0.125 exactly (denominator = 2³, only factor of 2).
**Common exact conversions to memorise** - 1/2 = 0.5; 1/4 = 0.25; 3/4 = 0.75 - 1/3 = 0.333...; 2/3 = 0.666... - 1/5 = 0.2; 2/5 = 0.4; 3/5 = 0.6; 4/5 = 0.8 - 1/8 = 0.125; 3/8 = 0.375; 5/8 = 0.625; 7/8 = 0.875 - 1/6 = 0.1666...; 5/6 = 0.8333... - 1/7 = 0.142857142857... (6-digit repeating cycle)
**Carpentry and construction** Imperial measurements use fractions heavily (1/16 inch, 3/8 inch). Many calculators and CNC machines, however, require decimal input. Converting 11/16" = 0.6875" is necessary when programming toolpaths.
**Mixed numbers** Mixed numbers (e.g., 2¾) are converted by treating the whole number separately: 2¾ = 2 + 3/4 = 2 + 0.75 = 2.75. The converter accepts input in the form "2 3/4" or "2+3/4".
Privacy: all calculations run in the browser. No data is transmitted.
Frequently Asked Questions
- 1/3 = 0.333... (repeating indefinitely). In decimal notation this is written 0.3̄ (bar over the 3) or 0.(3) to indicate the repeating block. It cannot be expressed as a terminating decimal because 3 (the denominator) has a prime factor other than 2 and 5. If you need a finite decimal approximation: 0.333 (3 decimal places) is accurate to within 0.1%; 0.3333333 is accurate to within 0.00001%.
- 0.625 = 625/1000 = 5/8. To derive this: 0.625 has 3 decimal places, so multiply by 10³ = 1000: 625/1000. GCD(625, 1000) = 125 (since 625 = 5⁴ and 1000 = 2³ × 5³, GCD = 5³ = 125). Divide: 5/8. Verification: 5 ÷ 8 = 0.625. Knowing 5/8 = 0.625 and 3/8 = 0.375 is useful in imperial measurement conversion (5/8 inch = 0.625 in = 15.875 mm).
- Find the LCM of the denominators (the Least Common Denominator), convert both fractions to that denominator, then add the numerators. Example: 1/4 + 1/6. LCM(4,6) = 12. Convert: 3/12 + 2/12 = 5/12. Reduce: GCD(5,12) = 1, so 5/12 is already in lowest terms. The decimal equivalent: 5 ÷ 12 = 0.41666... (0.4̄1̄6̄ repeating).
- Proper fraction: numerator < denominator (value between 0 and 1): 3/4, 5/8. Improper fraction: numerator ≥ denominator (value ≥ 1): 7/4, 11/3. Mixed number: whole number plus proper fraction: 1¾, 3⅔. To convert improper to mixed: divide and use the remainder: 7/4 = 1 remainder 3 = 1¾. To convert mixed to improper: multiply whole by denominator then add numerator: 1¾ = (1×4+3)/4 = 7/4.