Decimal to Fraction Calculator
Converts to simplest form with steps
Enter any decimal: 0.75, 1.333, 3.14159, −0.5
Common Decimals — Click to Convert
Click any decimal in the table below to convert it instantly.
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.5 | 1/2 | 50% |
| 0.25 | 1/4 | 25% |
| 0.75 | 3/4 | 75% |
| 0.333... | 1/3 | 33.3% |
| 0.666... | 2/3 | 66.7% |
| 0.125 | 1/8 | 12.5% |
| 0.375 | 3/8 | 37.5% |
| 0.625 | 5/8 | 62.5% |
| 0.875 | 7/8 | 87.5% |
| 0.2 | 1/5 | 20% |
| 0.4 | 2/5 | 40% |
| 0.6 | 3/5 | 60% |
| 0.8 | 4/5 | 80% |
| 0.1 | 1/10 | 10% |
| 0.01 | 1/100 | 1% |
Enter a decimal number to convert it to a fraction in simplest form.
Fraction (Simplest Form)
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1
Conversion Steps
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Fraction (simplified)
Mixed number
GCD used
Percentage
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How to Convert Decimals to Fractions
To convert a decimal to a fraction: (1) Count the decimal places. (2) Write the decimal digits as the numerator over 10 raised to the power of the decimal places as the denominator. (3) Simplify by dividing both numerator and denominator by their Greatest Common Divisor (GCD).
Example: 0.75. Two decimal places, so 75/100. GCD(75, 100) = 25. Divide both by 25: 75/25 = 3, 100/25 = 4. Result: 3/4.
Common Decimal Conversions
0.5 = 1/2. 0.25 = 1/4. 0.75 = 3/4. 0.333... = 1/3. 0.1 = 1/10. 0.2 = 1/5. 0.125 = 1/8. 0.375 = 3/8. 0.625 = 5/8. 0.875 = 7/8.
Simplifying Fractions
Find the GCD of numerator and denominator, then divide both by it. 12/16: GCD(12,16) = 4. 12/4 = 3, 16/4 = 4. Simplified: 3/4. A fraction is in simplest form when GCD = 1.
Mixed Number Form
When the decimal exceeds 1, convert to a mixed number. 2.75 = 2 and 3/4. The whole number is the integer part; the fraction is the decimal portion converted.
Repeating Decimals
0.333... = 1/3. 0.666... = 2/3. For repeating decimals, algebraic method: let x = 0.333..., 10x = 3.333..., subtract: 9x = 3, so x = 1/3.
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Decimal to Fraction Questions
How do I convert a decimal to a fraction?+
Three steps: (1) Count the decimal places. (2) Write the decimal digits as the numerator over 10 raised to the power of those decimal places. (3) Simplify by dividing both by their GCD. Example: 0.625 has 3 decimal places = 625/1000. GCD(625, 1000) = 125. 625/125 = 5, 1000/125 = 8. Answer: 5/8.
How do I convert a repeating decimal to a fraction?+
Use algebra. For 0.333...: let x = 0.333... Multiply by 10: 10x = 3.333... Subtract: 9x = 3. Divide: x = 3/9 = 1/3. For 0.142857... (repeating 6 digits): multiply by 10^6 and subtract to get x = 142857/999999 = 1/7. The number of nines in the denominator equals the number of repeating digits.
What is 0.75 as a fraction?+
0.75 = 75/100. GCD(75, 100) = 25. Simplified: 3/4. Verification: 3 ÷ 4 = 0.75. This is one of the most common decimal-to-fraction conversions. 0.75 = 75% = 3/4. Similarly: 0.25 = 1/4, 0.5 = 1/2.
How do I convert a fraction back to a decimal?+
Divide the numerator by the denominator. Examples: 3/4 = 3 ÷ 4 = 0.75. 1/3 = 1 ÷ 3 = 0.333... (repeating). 7/8 = 7 ÷ 8 = 0.875. 2/7 = 0.285714... (repeating 6-digit pattern). Terminating decimals come from fractions where the denominator has only 2s and 5s as prime factors.
What is 0.1 as a fraction?+
0.1 = 1/10 in simplest form. 0.01 = 1/100. 0.001 = 1/1000. For multiples: 0.3 = 3/10. 0.07 = 7/100. 0.004 = 4/1000 = 1/250 (GCD(4,1000) = 4; 4/4 = 1, 1000/4 = 250).
Can all decimals be written as fractions?+
Terminating decimals and repeating decimals can both be written as exact fractions — they are rational numbers. Non-repeating, non-terminating decimals (like π = 3.14159... or √2 = 1.41421...) are irrational and cannot be expressed as exact fractions. Only rational numbers can be represented as fractions.
What is the simplest form of a fraction?+
A fraction is in simplest form (lowest terms) when the numerator and denominator share no common factors other than 1. To simplify, divide both by their GCD. Example: 18/24. GCD(18,24) = 6. 18/6 = 3, 24/6 = 4. Simplest form: 3/4. You can check: GCD(3,4) = 1, so it cannot be simplified further.
What is 0.333 (not repeating) as a fraction?+
0.333 (terminating) = 333/1000. GCD(333, 1000) = 1. So it stays as 333/1000. This is subtly different from 0.333... (repeating), which equals exactly 1/3. 0.333 is 333/1000 = 0.333 exactly, while 1/3 = 0.333333... (infinite). The calculator treats input as terminating decimals unless you type the repeating form.
How do I convert a negative decimal to a fraction?+
Convert the absolute value to a fraction, then apply the negative sign. Example: −0.75 = −3/4. The process is identical: |−0.75| = 0.75 = 75/100 = 3/4. Add the negative sign: −3/4. Negative fractions can be written as −3/4, (−3)/4, or 3/(−4), which are all equivalent.
What decimal is 1/8?+
1/8 = 1 ÷ 8 = 0.125. The eighths: 1/8 = 0.125, 2/8 = 1/4 = 0.25, 3/8 = 0.375, 4/8 = 1/2 = 0.5, 5/8 = 0.625, 6/8 = 3/4 = 0.75, 7/8 = 0.875. These are common in measurement (inches, cooking). They all terminate because 8 = 2^3 (only factor of 2).