Decimal to Fraction Converter Formula

Understand the math behind the decimal to fraction converter. Each variable explained with a worked example.

Use the Decimal to Fraction Converter

Formulas Used

Approximate Numerator

approx_numerator = round(decimal_val * max_denom) / gcd(round(decimal_val * max_denom), max_denom)

Approximate Denominator

approx_denominator = max_denom / gcd(round(decimal_val * max_denom), max_denom)

Verification (decimal)

verification = (round(decimal_val * max_denom) / gcd(round(decimal_val * max_denom), max_denom)) / (max_denom / gcd(round(decimal_val * max_denom), max_denom))

Variables

VariableDescriptionDefault
decimal_valDecimal Value0.375
max_denomMax Denominator1000

How It Works

Decimal to Fraction Converter

Method

1. Multiply the decimal by the max denominator 2. Round to the nearest integer to get the numerator 3. Use the GCD (Greatest Common Divisor) to simplify 4. Divide both numerator and denominator by the GCD

Example: 0.375 with max denominator 1000 → 375/1000 → GCD(375,1000) = 125 → 3/8

Worked Example

Convert 0.375 to a fraction.

decimal_val = 0.375max_denom = 1000
  1. 010.375 × 1000 = 375 (numerator before simplification)
  2. 02GCD(375, 1000) = 125
  3. 03Numerator = 375 / 125 = 3
  4. 04Denominator = 1000 / 125 = 8
  5. 05Result: 3/8

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