Decimal to Fraction Calculator
Convert any decimal to a simplified fraction with step-by-step work.
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How to Convert a Decimal to a Fraction
Every decimal number can be expressed as a fraction. The method depends on whether the decimal is terminating (ends after a fixed number of digits) or repeating (a digit or group of digits repeats infinitely).
Terminating Decimals
For a terminating decimal like 0.75: count the decimal places (2 in this case), write the decimal as a numerator over 10^(number of places) as the denominator (75/100), then simplify by dividing by the GCF. 75/100 ÷ 25 = 3/4.
Repeating Decimals
For a repeating decimal like 0.333...: let x = 0.333... Multiply both sides by 10: 10x = 3.333... Subtract: 9x = 3, so x = 3/9 = 1/3. For longer repeating blocks, multiply by the appropriate power of 10.
Mixed Decimals
For a number like 2.5: separate the whole number (2) and decimal part (0.5). Convert 0.5 = 1/2. Result: 2½ or as an improper fraction, 5/2.
Decimal-to-fraction conversion is useful in cooking (measuring ingredients in thirds and quarters), woodworking, and any context where exact fractions are more meaningful than rounded decimals.
Step-by-Step Example: Converting 0.375
Step 1 — Count decimal places: 0.375 has 3 decimal places.
Step 2 — Write as a fraction over 10³ = 1000: 375/1000.
Step 3 — Find the GCF of 375 and 1000. Both are divisible by 5: 375/5 = 75, 1000/5 = 200. Both are still divisible by 5: 75/5 = 15, 200/5 = 40. Both are divisible by 5 again: 15/5 = 3, 40/5 = 8. GCF = 125.
Step 4 — Divide numerator and denominator by 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8. Result: 3/8.
Common Decimal to Fraction Reference
| Decimal | Fraction | Simplified |
|---|---|---|
| 0.1 | 1/10 | 1/10 |
| 0.25 | 25/100 | 1/4 |
| 0.333... | 3/9 | 1/3 |
| 0.5 | 5/10 | 1/2 |
| 0.75 | 75/100 | 3/4 |
| 0.8 | 8/10 | 4/5 |
| 0.125 | 125/1000 | 1/8 |
Frequently Asked Questions
0.5 has 1 decimal place, so write as 5/10. Simplify by dividing by GCF (5): 1/2.
Let x = 0.333... Then 10x = 3.333... Subtract: 9x = 3, so x = 3/9 = 1/3.
0.625 = 625/1000. GCF of 625 and 1000 is 125. Simplified: 5/8.
1.75 = 175/100 = 7/4 (simplified). As a mixed number: 1¾.
Every terminating or repeating decimal is a rational number and can be expressed as a fraction. Non-terminating, non-repeating decimals (like π or √2) are irrational and cannot be written as exact fractions.
2.6 = 26/10. Simplify by dividing by 2: 13/5. As a mixed number: 2 3/5. You can verify: 13 ÷ 5 = 2.6.
Let x = 0.142857142857... Since the block "142857" repeats over 6 digits, multiply both sides by 10⁶ = 1,000,000: 1000000x = 142857.142857... Subtract: 999999x = 142857, so x = 142857/999999 = 1/7.