Fraction to Decimal Calculator
Convert proper and improper fractions or mixed numbers into terminating or repeating decimals.
Fraction to Decimal โ interactive calculator, computed instantly in your browser.
Guide to Converting Fractions to Exact Decimals & Percentages
Fraction to Decimal Anatomy: Terminating vs Repeating
Rule of 2 and 5: In simplest form, a fraction produces a finite terminating decimal if and only if the prime factorization of its denominator contains only 2s and/or 5s.
Converting a common fraction into a decimal is accomplished by dividing the numerator (top number) by the denominator (bottom number). Decimals are easier to compare, compute in electronic hardware, and apply in financial and engineering metrics.
1. Conversion Methodology
To convert any proper or improper fraction $\frac{a}{b}$ into decimal format:
For mixed numbers $W \frac{N}{D}$, convert to an improper fraction first: $\frac{W \times D + N}{D}$, then divide by $D$.
2. Comprehensive Fraction to Decimal Reference Chart
| Fraction | Decimal Equivalent | Percentage (%) | Type |
|---|---|---|---|
| 1/2 | 0.5 | 50.0% | Terminating |
| 1/3 | 0.3333... (0.3ฬ) | 33.33% | Repeating |
| 1/4 | 0.25 | 25.0% | Terminating |
| 1/5 | 0.2 | 20.0% | Terminating |
| 1/8 | 0.125 | 12.5% | Terminating |
| 3/8 | 0.375 | 37.5% | Terminating |
| 1/16 | 0.0625 | 6.25% | Terminating (Machinist standard) |
๐ Fraction & Decimal Number Systems
Converting rational fractions to decimal equivalents enables swift engineering and financial calculations. Explore our โ Math Hub for complete fraction tools.
Convert decimals back to simplified fractions or perform mixed fraction operations below.
Frequently Asked Questions (Fraction to Decimal)
Our standard number system is base-10 (factors 2 and 5). If a simplified fraction has any prime factor other than 2 or 5 in its denominator (like 3, 7, 11, or 13), it cannot divide evenly into powers of 10 and forms a repeating pattern.
Keep the whole number as the integer part of the decimal, then divide the fractional numerator by denominator to form the digits after the decimal point. For example, $4 \frac{3}{5} = 4 + (3 \div 5) = 4.6$.