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Arithmetic Precision
Fraction to Decimal Calculator (& Decimal to Fraction)
Convert fractions to exact decimals, percentages, and mixed numbers, or reverse-convert any decimal into a fully simplified lowest-term fraction with step-by-step reduction.
1 Convert Fraction to Decimal
/
Decimal & Percentage:
37.5%
0.375
2 Convert Decimal to Simplified Fraction
Simplified Fraction:
Proper Fraction
5 / 8
Converting Between Fractions & Decimals
A fraction represents a part of a whole, expressed as a numerator over a non-zero denominator (a / b). A decimal is an expression of fractional parts using powers of 10 in standard positional notation.
Core Mathematical Methods
Fraction to Decimal: Divide Numerator by Denominator (a ÷ b)
Decimal to Fraction: Multiply by 10^k / 10^k, then simplify by GCD
Step-by-Step Example: Decimal to Fraction
Suppose you want to convert 0.375 into its lowest simplified fraction:
- Count the decimal places: 0.375 has 3 decimal places, so the initial denominator is 10³ = 1,000.
- Write as an unsimplified fraction:
375 / 1000. - Find the Greatest Common Divisor (GCD) of 375 and 1,000, which is 125.
- Divide both numbers by 125:
(375 ÷ 125) / (1000 ÷ 125) = 3 / 8.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/3 | 0.3333... | 33.33% |
Frequently Asked Questions
Division by zero is mathematically undefined. A fraction must always have a non-zero denominator.
If the decimal is greater than 1 (such as 2.75), the integer portion (2) separates out, and the fractional portion (0.75) simplifies to 3/4, yielding the mixed number 2 3/4 or improper fraction 11/4.
Educational Disclaimer: Local JavaScript math execution uses IEEE-754 double precision standard.