Decimal to Fraction Converter
To convert a decimal to fraction, write the decimal over 1, multiply both by 10 for each decimal place, then simplify. Example: 0.75 = 75/100 = 3/4. For repeating decimals like 0.333... use algebra: x = 0.333..., 10x = 3.333..., 9x = 3, x = 1/3.
Convert decimals to fractions. Shows simplified fraction and mixed number form. Visual representation of the fraction.
Enter Decimal
Common Decimals Reference
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.125 | 1/8 | 12.5% |
| 0.25 | 1/4 | 25% |
| 0.333... | 1/3 | 33.33% |
| 0.5 | 1/2 | 50% |
| 0.666... | 2/3 | 66.67% |
| 0.75 | 3/4 | 75% |
How to Use
- 1
Enter decimal
Input the decimal number you want to convert
- 2
View fraction
See the equivalent fraction in lowest terms
- 3
Copy result
Copy the fraction to use in your calculations
Frequently Asked Questions
- How do I convert a decimal to a fraction?
- Write the decimal over a power of 10 based on decimal places: 0.75 = 75/100, 0.125 = 125/1000. Then simplify by finding GCD. 75/100: GCD is 25, so 75÷25/100÷25 = 3/4. For repeating decimals, use algebra: if x = 0.333..., then 10x = 3.333..., so 9x = 3, x = 1/3.
- How do I simplify a fraction?
- Find the Greatest Common Divisor (GCD) of numerator and denominator, then divide both by it. For 48/64: factors of 48 are 1,2,3,4,6,8,12,16,24,48; factors of 64 are 1,2,4,8,16,32,64. GCD is 16. 48÷16/64÷16 = 3/4.
- What are common decimal to fraction conversions?
- Common conversions: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.333... = 1/3, 0.666... = 2/3, 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8, 0.875 = 7/8, 0.2 = 1/5, 0.1 = 1/10, 0.0625 = 1/16.
- How do I convert repeating decimals to fractions?
- For repeating decimals: 0.333... = 1/3, 0.666... = 2/3, 0.111... = 1/9. General method: if x = 0.abab... (2 repeating digits), multiply by 100: 100x = ab.abab..., subtract: 99x = ab, so x = ab/99. Example: 0.363636... = 36/99 = 4/11.
- Why are fractions sometimes more accurate than decimals?
- Some fractions cannot be expressed exactly as decimals: 1/3 = 0.333... (infinite). In calculations, using fractions preserves precision. Computers store decimals with limited precision (floating-point errors), so 0.1 + 0.2 might equal 0.30000000000000004 instead of 0.3.
- How do I convert unusual repeating decimals like 0.36363... or 0.54545...?
- 0.36363... = 36/99 = 4/11. 0.54545... = 54/99 = 6/11. Pattern: two-digit repeating block ab → ab/99, then simplify. For 0.31496... (non-repeating), count 5 decimal places → 31496/100000 → simplify by GCD. 0.104 = 104/1000 = 13/125. 0.543 = 543/1000 (already simplified, GCD=1).
- What is 0.36363 as a fraction?
- 0.36363 as a terminating decimal equals 36363/100000 (GCD is 1, already simplified). If the decimal repeats (0.363636...), the exact fraction is 4/11 — verify: 4 ÷ 11 = 0.363636... The repeating two-digit block 36 gives 36/99, which simplifies to 4/11. Most calculators and tools showing "0.36363" intend the repeating form, so 4/11 is typically the answer.
- What is 0.104 as a fraction?
- 0.104 as a fraction is 13/125. Write 104/1000 (three decimal places = denominator 1,000), then divide both by their GCD of 8: 104 ÷ 8 = 13, 1000 ÷ 8 = 125. Check: 13 ÷ 125 = 0.104 ✓. Fully simplified because 13 is prime and 125 = 5³ share no factors.
- What is 0.668 as a fraction?
- 0.668 as a fraction is 167/250. Write as 668/1000, then divide by GCD of 4: 668 ÷ 4 = 167, 1000 ÷ 4 = 250. Since 167 is prime and 250 = 2 × 5³, they share no factors, so 167/250 is fully simplified. Check: 167 ÷ 250 = 0.668 ✓.
- What is 0.31496 as a fraction?
- 0.31496 as a fraction is 3937/12500. Write as 31496/100000 (five decimal places), then divide by GCD of 8: 31496 ÷ 8 = 3937, 100000 ÷ 8 = 12500. GCD(3937, 12500) = 1, so 3937/12500 is fully simplified. This value appears in unit conversions: 8 mm = 0.31496 inches.
- What is 0.159 or 0.1590 as a fraction?
- 0.159 as a fraction is 159/1000. Write as 159/1000 (three decimal places). Since 159 = 3 × 53 and 1000 = 2³ × 5³ share no common factors, GCD = 1 and 159/1000 is fully simplified. The trailing zero in 0.1590 makes no difference: 0.1590 = 0.159 = 159/1000.
- What is 0.0787402 as a fraction?
- 0.0787402 as a fraction is 393701/5000000. Write as 787402/10000000 (seven decimal places), then divide by GCD of 2: 787402 ÷ 2 = 393701, 10000000 ÷ 2 = 5000000. Since 393701 is odd and not divisible by 5, the fraction is fully simplified. This value arises in engineering: 2 mm = 0.0787402 inches (since 1 mm = 0.0393701 in).