Decimal to Fraction
Convert standard decimals and repeating decimals back into fractions. Get instant step-by-step solutions — completely free, no signup required.
Free Decimal to Fraction Calculator
Enter your problem below to get an instant step-by-step solution.
About Decimal to Fraction
Convert standard decimals and repeating decimals back into fractions. Fractions represent parts of a whole and are fundamental to arithmetic, algebra, and real-world calculations like cooking, finance, and measurement.
Our Decimal to Fraction calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any decimal to fraction expression and receive a complete, verified solution with every step shown.
Decimal to Fraction Formula
0.d₁d₂…dₙ = d₁d₂…dₙ / 10ⁿ (then simplify)
To convert a terminating decimal, write the digits over the matching power of ten and reduce by the greatest common divisor. For a repeating decimal, set it equal to x, multiply by a power of ten to shift one full repeat, and subtract to cancel the repeating part.
Worked Example
Convert 0.3̅6̅ (0.363636…) to a fraction
- Let x = 0.3636…
- The repeat has 2 digits, so 100x = 36.3636…
- Subtract: 100x − x = 36, so 99x = 36
- x = 36/99 = 4/11
Answer: 4/11
Common Mistakes to Avoid
- Not simplifying the final fraction.
- Multiplying by 10 when the repeat has two digits (use 100).
- Treating a rounded decimal such as 0.33 as exactly 1/3.
How to Use the Decimal to Fraction Calculator
- 1
Type your Decimal to Fraction problem into the input field above
- 2
Press Enter or click the Solve button to run the calculation
- 3
Review the step-by-step solution that appears below the input
- 4
Check the breakdown of each operation to understand the method
- 5
Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Decimal to Fraction formula?
0.d₁d₂…dₙ = d₁d₂…dₙ / 10ⁿ (then simplify). To convert a terminating decimal, write the digits over the matching power of ten and reduce by the greatest common divisor. For a repeating decimal, set it equal to x, multiply by a power of ten to shift one full repeat, and subtract to cancel the repeating part.
Can you show a worked Decimal to Fraction example?
Convert 0.3̅6̅ (0.363636…) to a fraction: Let x = 0.3636…; The repeat has 2 digits, so 100x = 36.3636…; Subtract: 100x − x = 36, so 99x = 36; x = 36/99 = 4/11. Answer: 4/11.
Is this Decimal to Fraction calculator free to use?
Yes — the Decimal to Fraction calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Decimal to Fraction homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.