Decimal To Fraction Calculator
Every terminating decimal is a fraction in disguise: the digits after the point tell you the denominator. The decimal 0.375 has three decimal places, so it is 375 thousandths, or 375/1000, which simplifies to 3/8. Repeating decimals work differently and need a short piece of algebra, which is why this calculator has a dedicated repeating mode.
Enter any decimal below for an exact conversion in lowest terms, or switch to repeating mode and tell the tool which trailing digits repeat. You get the simplified fraction, the mixed number, the percentage, a decimal check, and every step of the working. A third mode runs the conversion in reverse, turning a fraction or mixed number back into a decimal and marking any repeating block in parentheses.
Exact results for terminating and repeating decimals. A decimal that never terminates and never repeats, such as pi, has no exact fraction form.
Quick Answer
Key takeaways
- Decimal places set the denominator: one place is tenths, two is hundredths, three is thousandths. Simplify once with the greatest common factor to reach lowest terms.
- Terminating and repeating decimals are different inputs. 0.333 is 333/1000, while 0.333… is exactly 1/3, so pick the mode that matches the number you actually have.
- Repeating conversions use algebra, not rounding: multiply, subtract so the repeating tails cancel, then solve and simplify.
- The reverse mode marks repeating blocks in parentheses, so 1/6 reads as 0.1(6) instead of a rounded 0.167.
How to use the decimal to fraction calculator
Start with the conversion type. Leave it on terminating decimal for an ordinary decimal that ends, type the number, and press Convert. The result box shows the simplified fraction as the main number, then the mixed number, the percentage, a decimal check, and the numbered steps that produced it.
For a repeating decimal, switch the type, type the decimal as you see it, and enter how many trailing digits repeat. For 0.1666… you type 0.1666 and enter 1, because only the 6 repeats. For 0.363636… you type 0.36 and enter 2. Getting that count right is the whole job: it tells the algebra where the repeating block starts. If you then want to work with the fraction you found, the fraction addition calculator adds, subtracts, multiplies, and divides fractions with the same lowest-terms discipline.
The third mode reverses direction. Enter a fraction like 1/3 or a mixed number like 1 1/2 and the tool runs the long division, watching the remainders. When a remainder repeats, the digits from that point repeat forever, and the tool writes them in parentheses instead of rounding the answer away.
The formulas behind each mode
The terminating method works because our number system is base 10: each place after the point is a tenth of the one before it, so three places are thousandths by definition. The greatest common factor step is not cosmetic. A fraction like 375/1000 and its reduced form 3/8 are the same value, but lowest terms are the standard form teachers, textbooks, and machinists expect, and smaller numbers are easier to compare and to measure. The method is the one taught in standard pre-algebra courses, such as the OpenStax Prealgebra coverage of decimals and fractions listed in the references.
Repeating decimals cannot use place value alone, because the digits never end. Algebra solves that: multiplying by the right powers of 10 produces two numbers with identical repeating tails, and subtracting removes the infinite part entirely, leaving an ordinary equation. That is also the proof that every repeating decimal is a rational number, a point the University of Toronto Mathematics Network explains in its question corner on recurring decimals, linked below.
Worked examples, checked against the tool
The calculator is pre-filled with the first case, and every figure below is what it returns.
| Input | Mode | Result | Other forms |
|---|---|---|---|
| 0.375 | Terminating | 3/8 | 37.5%, check 0.375 |
| 0.1666, 1 repeating digit | Repeating | 1/6 | 16.6667% |
| 1/3 | Fraction to decimal | 0.(3) | Block "3" repeats forever |
| 1e-7 | Terminating | 1/10000000 | Expanded to 0.0000001 first |
For 0.375, the steps the tool shows are: count the decimal places (three, so write it over 1000 as 375/1000), find the greatest common factor of 375 and 1000 (125), divide both parts by 125 to reach 3/8, and check that 375 / 1000 returns the original 0.375.
Let x = 0.1666… typed as 1666 with the last 1 digit repeating, exactly as the tool lists it in its first step.
Multiply by 1000 to move the 3 non-repeating digits left: 1000x = 166.66…
Multiply by 10000 to move one full repeating block further: 10000x = 1666.66…
Subtract: 9000x = 1500, so x = 1500/9000. Simplify with GCF 1500 to get 1/6.
That subtraction is the heart of the method. Both products end in the same endless string of 6s, so the infinite part cancels and only whole numbers remain. Once you have the fraction form, its percentage form in the results table is the same conversion you would do by hand, and the average of percentages calculator is a useful next step when several converted percentages need to be combined.
Quick reference: common decimals as fractions
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.5 | 1/2 | 0.125 | 1/8 |
| 0.25 | 1/4 | 0.375 | 3/8 |
| 0.75 | 3/4 | 0.625 | 5/8 |
| 0.2 | 1/5 | 0.875 | 7/8 |
| 0.4 | 2/5 | 0.1 | 1/10 |
| 0.6 | 3/5 | 0.333… | 1/3 |
| 0.8 | 4/5 | 0.666… | 2/3 |
| 0.0625 | 1/16 | 0.1666… | 1/6 |
The eighths row is worth memorizing if you work with a tape measure or a kitchen scale: each eighth is 0.125, so any measurement in eighths converts by counting multiples of 125 thousandths. The thirds and sixths cannot be written exactly as finite decimals at all, which is why they appear here with trailing dots and why the repeating mode exists.
What competing decimal to fraction calculators miss
Miss 1: repeating decimals get rounded or refused. Several top-ranking tools, including the Webby and MathsIsFun guides reviewed for this page, explain the algebra for a repeating decimal in prose but only convert the finite digits you type, which quietly turns 0.333… into 333/1000. This calculator has a real repeating mode: you state how many trailing digits repeat and it runs the multiply, subtract, and simplify steps for you.
Miss 2: no reverse direction. CalculatorSoup handles repeating input well, but a fraction to decimal question sends you to a separate tool. Here the reverse mode sits in the same card, runs the long division, detects the repeating remainder, and writes the answer as 0.(3) or 0.1(6) instead of a rounded decimal.
Miss 3: scientific notation breaks the conversion. Small values copied from a spreadsheet or a lab instrument often arrive as 1e-7. Tools that read that literally return 0/1 or an error. This calculator expands e-notation to 0.0000001 first, then converts it correctly to 1/10000000, as the worked examples table shows.
Miss 4: an answer with no auditable steps. A bare fraction cannot be checked. Every mode here lists its steps in order, including the GCF used, so a student can copy the working into homework and a tradesperson can verify the measurement before cutting.
Frequently Asked Questions
Use algebra: call the decimal x, multiply by powers of 10 until the repeating blocks line up, subtract so the repeating tails cancel, and solve for x. For 0.1666… with the 6 repeating, 10000x – 1000x = 1500 gives x = 1500/9000 = 1/6. The calculator shows these steps for any repeating input.
0.75 = 75/100, and the greatest common factor of 75 and 100 is 25, so it simplifies to 3/4.
No. The terminating decimal 0.333 is exactly 333/1000. The repeating decimal 0.333… equals 1/3. They differ by 1/3000, which matters in precise work, so use the repeating mode for repeating decimals.
Convert the positive part first, then put the minus sign back in front. For -1.25: 1.25 = 125/100 = 5/4, so -1.25 = -5/4, or -1 1/4 as a mixed number.
75/100 and 3/4 name the same value, but 3/4 is the standard lowest-terms form: smaller numbers, easier to compare, and what teachers and textbooks expect. The GCF is the largest number dividing both parts, so one division finishes the job.
Yes. Change the conversion type to fraction to decimal and enter something like 1/3 or 1 1/2. The tool performs the long division and, when the remainders start repeating, shows the repeating block in parentheses: 1/3 becomes 0.(3) and 1/6 becomes 0.1(6).
Every terminating or repeating decimal is a rational number and converts exactly. Decimals that never terminate and never repeat, like pi or the square root of 2, are irrational and have no exact fraction form, only approximations.
It expands it first. 1e-7 becomes 0.0000001, which converts to 1/10000000. Small or large values typed in e-notation are handled the same way as if you had typed the full decimal.
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References
- OpenStax, Rice University, Prealgebra 2e, the decimals and fractions chapters covering place-value conversion and simplification to lowest terms. OpenStax: Prealgebra 2e. Accessed October 2026.
- National Institute of Standards and Technology, Guide for the Use of the International System of Units, Appendix B on decimal and fractional quantity expression. NIST: SI Unit Guide (SP 811). Accessed October 2026.
- University of Toronto Mathematics Network, Question Corner on expressing a repeating decimal number as a fraction, including the geometric series justification. University of Toronto: Repeating Decimals as Fractions. Accessed October 2026.
- Math is Fun, Converting Decimals to Fractions, a worked place-value method with the 0.75 and 0.625 examples used as a teaching cross-check. Math is Fun: Convert Decimals to Fractions. Accessed October 2026.
- Khan Academy, Arithmetic course material on converting fractions to decimals and repeating decimal notation. Khan Academy: Arithmetic. Accessed October 2026.