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Decimal To Fraction

Converting decimals to fractions reveals the exact rational representation of a number, essential for precision work in cooking, carpentry, and engineering where fractions are the standard unit. Our converter handles terminating decimals (0.75 → 3/4), repeating decimals (0.333... → 1/3), and shows the simplification steps.

Fraction

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About the Decimal to Fraction Converter

Converting decimals to fractions reveals the exact rational representation of a number, essential for precision work in cooking, carpentry, and engineering where fractions are the standard unit. Our converter handles terminating decimals (0.75 → 3/4), repeating decimals (0.333... → 1/3), and shows the simplification steps.

How to use it

  1. Enter any decimal number (e.g., 0.625, 3.14, 0.1666...).
  2. See the exact fraction in lowest terms.
  3. For repeating decimals: indicate with a bar or ellipsis (0.3... or 0.142857142857...).
  4. See step-by-step simplification via GCD.

Formula & methodology

Terminating decimal: multiply by 10^n (where n = decimal places) to get integer, use that as numerator over 10^n, simplify. Example: 0.625 = 625/1000 = 5/8. Repeating decimal: let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, x = 1/3. Mixed: combine integer part with fraction.

Common use cases

  • Carpentry: converting 0.375 inches to 3/8 inch for ruler reading
  • Cooking: converting 0.25 cups to 1/4 cup measurement
  • Engineering drawings: converting decimal dimensions to fractional tolerances
  • Math: simplifying calculator outputs to exact rational form
  • Finance: converting decimal interest rates to fractional form

Frequently asked questions

Every terminating and repeating decimal can be expressed as a fraction (rational number). Terminating decimals like 0.5, 0.125, and 0.75 have exact fractional forms. Repeating decimals like 0.333... = 1/3 and 0.142857... = 1/7 are also rational. Non-repeating, non-terminating decimals (like π = 3.14159... or √2 = 1.41421...) are irrational — they cannot be expressed as any fraction.
It is exactly equal, not approximately. Proof: let x = 0.999...; then 10x = 9.999...; subtract: 9x = 9; x = 1. Another proof: 1/3 = 0.333...; multiply both sides by 3: 1 = 0.999... The infinite sum 9/10 + 9/100 + 9/1000... = 9 × (1/10)/(1−1/10) = 9 × (1/9) = 1. This surprises many people, but it is a rigorous mathematical fact, not a rounding approximation.

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