What is Decimal to Fraction Conversion?

Decimal to Fraction conversion expresses a decimal number as a simplified fraction. The conversion: count decimal places to get denominator power of 10, then simplify by dividing both numerator and denominator by their GCD. Useful for: converting calculator output to fraction form (homework answers), recipe measurements (0.75 cup → 3/4 cup), exact mathematical answers (often required in tests), engineering specifications, time calculations (0.5 hour → 1/2 hour). Reverse mode also supported: enter fraction, get decimal.

How to use this tool

1. Choose direction — Decimal → Fraction OR Fraction → Decimal.
2. Enter your number — Decimal value OR numerator + denominator.
3. View converted result — Simplified fraction or decimal output.
4. Read approximation note — Recurring decimals approximate; non-terminating decimals lose precision.

Decimal to fraction algorithm

1. Separate whole part: 3.75 → 3 + 0.75
2. Decimal part as fraction: count decimal places. 0.75 has 2 decimal places, so denominator = 100. Numerator = 75 → 75/100
3. Simplify with GCD: gcd(75, 100) = 25. 75/100 = 3/4
4. Combine: 3.75 = 3 + 3/4 = 3 3/4 (mixed) or 15/4 (improper)

Recurring decimals (0.333… = 1/3):

Tool can't detect recurring — treats as 333/1000 or similar approximation. For exact recurring conversion, use mathematical analysis.

Examples

• 0.5: → 1/2
• 0.75: → 3/4
• 0.125: → 1/8
• 3.14: → 157/50
• 0.333… (approx): → 333/1000 (not exact 1/3)
• 1/6 as decimal: → 0.166666… (recurring)

Tips & best practices

• For exact fractions: round decimal first (0.333 → 0.333 → 333/1000, but 1/3 is exact)
• Some decimals are terminating (0.5, 0.25); others recurring (0.333…, 0.142857…)
• Tool handles terminating decimals exactly; recurring approximated
• For tests requiring exact fractions, use math knowledge for common recurrings

Frequently Asked Questions

Why isn't 0.333 = 1/3?

0.333 (three decimal places) = 333/1000. True 1/3 = 0.333333… (infinite repeating). Tool can't detect this without explicit notation.

What's recurring decimal?

Decimals that go on forever in a pattern: 1/3 = 0.333…, 2/7 = 0.285714285714… All fractions either terminate or recur.

Can I get exact 1/3?

Enter as fraction (numerator 1, denominator 3). Decimal output shows 0.333333… (10 digits). Reverse to fraction requires algebraic recognition.

Largest fraction supported?

JavaScript integer limit (~9 quadrillion). Sufficient for any practical use.

Related tools

Fraction Calculator · Percentage Calculator · GCD & LCM Calculator