Solve recurring decimals with exact fraction steps. Handle mixed, pure, and repeating patterns with confidence. Plot decimal cycles, download records, and learn conversions clearly.
| Decimal notation | Type | Exact fraction | Notes |
|---|---|---|---|
| 0.(3) | Pure recurring | 1 / 3 | Single digit repeats forever. |
| 0.1(6) | Mixed recurring | 1 / 6 | One fixed digit appears before repetition. |
| 2.(45) | Pure recurring | 27 / 11 | Integer part stays outside the repeating cycle. |
| 3.12(7) | Mixed recurring | 563 / 180 | Two non-repeating digits precede the cycle. |
Let the number be written as I.N(R).
Here, I is the integer part, N is the non-repeating block, and R is the repeating block.
If the non-repeating length is m and the repeating length is k, then the exact fraction is:
x = (P − Q) / (10^m × (10^k − 1))
Where:
P = integer formed by concatenating I, N, and R
Q = integer formed by concatenating I and N
For a terminating decimal, the fraction becomes integer digits / 10^m, then reduces normally.
Enter the number in decimal notation such as 4.2(17), or fill the integer, non-repeating, and repeating fields manually.
Choose how many decimal places to preview and how many digit points to plot on the chart.
Press Calculate to show the exact fraction, unreduced fraction, mixed number, cycle length, and decimal preview above the form.
Use the CSV button to save a structured data file. Use the PDF button to save the displayed result block as a document.
A recurring decimal has one digit or a block of digits that repeats forever after the decimal point. Examples include 0.(3), 1.2(45), and 7.(81).
A pure recurring decimal starts repeating immediately after the decimal point. A mixed recurring decimal has one or more non-repeating digits before the recurring block begins.
Yes. The calculator uses an exact algebraic conversion method, then reduces the result to lowest terms. This avoids approximation errors from rounded decimal values.
The unreduced fraction shows the direct algebraic setup. The reduced fraction gives the simplest equivalent form, which is usually the final answer expected in maths work.
Yes. If you leave the repeating block empty, the tool treats the value as terminating. It still converts the decimal into an exact fraction and simplifies it.
Use parentheses around the repeating block. For example, write 0.(3), 5.1(27), or 12.34(56). This clearly identifies which digits repeat forever.
The graph plots the first digits after the decimal point. Repeating decimals create a recurring visual pattern, which helps confirm the cycle and its length.
The CSV download contains key result fields in rows. The PDF button captures the displayed result section, including the summary values and worked conversion steps.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.