Decimal to Fraction
Convert any decimal—terminating or repeating—into a precise fraction.
Enter a standard decimal value like 0.25 or 1.5.
Start Converting
Enter a decimal to see its exact fractional form and the algebraic steps.
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Why Convert Decimals to Fractions?
Decimals are widely used in currency and digital data, but fractions are the language of precision. In fields like carpentry, cooking, and algebra, "close enough" isn't good enough. 0.33 is an approximation, but 1/3 is exact. Our Decimal to Fraction Calculator bridges this gap, instantly converting any decimal—even tricky infinite ones—into its precise fractional form.
Advanced Conversion Features
Terminating Decimals
Handles finite decimals like 0.75 or 0.125. Automatically places them over 10, 100, or 1000 and simplifies.
Repeating Decimals
The only tool that easily handles 0.333... or 0.166... using advanced algebra to find the exact root fraction (1/3, 1/6).
Auto-Simplification
Never get a raw answer like "50/100". We calculate the Greatest Common Divisor to always show "1/2".
Step-by-Step Proofs
See the math. We show the exact algebra method used to solve for X, perfect for students checking homework.
Mixed Number Support
Input "1.5" to get both "3/2" (Improper) and "1 1/2" (Mixed), giving you flexibility for any project.
100% Precision
Avoid rounding errors. By converting to fractions, you maintain the infinite precision of the number.
How to Use This Tool
- 1
Identify if your decimal terminates (ends) or repeats.
- 2
Enter the base decimal (e.g. 0.1) in the left field.
- 3
If it repeats, toggle the 'Repeating' switch and enter the repeating digits in the second box.
- 4
Instantly view the simplified fraction and the mixed number.
- 5
Expand the 'Solution Steps' card to see the algebraic proof.
Real-World Applications
Construction & DIY
Tape measures don't use decimals; they use 1/16ths and 1/32nds. Convert blueprint dimensions like "5.375 inches" to "5 3/8 inches" to make accurate cuts.
Math Homework
Algebra often requires answers in "exact form" (fractions). Use this to verify that your manual conversion of 0.666... resulted in the correct 2/3.
Cooking & Baking
Digital scales might say "0.25 kg", but your recipe calls for fractions of a cup. Quickly convert measurements to match your measuring cups.
Stock Market & Odds
Probabilities and historical stock quotes are often expressed in fractions. Convert percentage decimals to fractional odds easily.
Common Conversions Cheat Sheet
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.5 | 1/2 |
| 0.666... | 2/3 |
| 0.75 | 3/4 |
Avoid These Mistakes
- Ignoring the RepeatTreating 0.333 as 333/1000 instead of 1/3. If the decimal repeats, you must use the repeating logic.
- Not SimplifyingLeaving an answer as 5/10 instead of 1/2. Always reduce to the lowest terms for the correct final answer.
- Miscounting ZerosFor 0.05, the denominator is 100 (two zeros), not 10. Count the decimal places carefully!
Frequently Asked Questions
How do you convert a decimal to a fraction?
To convert a terminating decimal (like 0.75), write it as 75/100 and simplify. Divide both numbers by their Greatest Common Divisor (25) to get 3/4. For mixed numbers like 1.5, write the whole number (1) and convert the decimal .5 to 1/2, giving 1 1/2.
How do you convert repeating decimals (like 0.666...)?
For repeating decimals, use algebra. Let x = 0.666... Multiply by 10 to get 10x = 6.666... Subtract x from 10x (10x - x = 9x) and 0.666... from 6.666... (leaving 6). So, 9x = 6, meaning x = 6/9, which simplifies to 2/3. Our tool does this automatically.
What is the difference between terminating and repeating decimals?
A terminating decimal ends after a few digits (e.g., 0.125 = 1/8). A repeating decimal goes on forever with a repeating pattern (e.g., 0.1666... = 1/6). Rational numbers can always be written as fractions, whether they terminate or repeat.
Why does 0.333... equal 1/3?
When you divide 1 by 3 using long division, you get 0.333... going on forever. Therefore, the fraction 1/3 is the exact representation of that infinite decimal. Approximating it as 0.33 is close, but not exact math.
Can this calculator handle mixed numbers?
Yes! If you enter a value greater than 1, like 2.5, the calculator displays the result as both an improper fraction (5/2) and a mixed number (2 1/2), so you can use whichever format fits your needs.
What is 0.001 as a fraction?
0.001 has three decimal places, so the denominator is 1,000. It converts to 1/1,000.
Is this tool useful for construction?
Absolutely. Tape measures use fractions (1/8, 1/16, 1/32). Conversion is essential when digital blueprints show 5.375 inches but you need to find 5 3/8 inches on your ruler.
How accurate is the conversion?
It is 100% accurate. Unlike basic calculators that might round 1/3 to 0.333333, our algorithm treats repeating decimals as infinite series to find the exact fractional root.
Does it simplify the result automatically?
Yes. If you enter 0.5, you won't get 5/10. The tool automatically finds the Greatest Common Divisor (GCD) and reduces it to 1/2.
What is the Golden Ratio as a fraction?
The Golden Ratio (Phi) is an irrational number approx 1.618..., meaning it cannot be written as a simple fraction. However, consecutive Fibonacci numbers (like 8/5, 13/8, 21/13) approximate it increasingly well.