Repeating Decimal Converter Calculator

Turn repeating decimals into fractions, ratios, and percentages. See simplification steps, previews, and place-value details. Built for students, teachers, and precise number conversions daily.

Enter Repeating Decimal Values

Formula Used

Notation: Let the number be W.N(R).

W is the whole part, N is the non-repeating block, and R is the repeating block.

m = number of digits in N, and n = number of digits in R.

A = integer formed by writing W, N, and R together.

B = integer formed by writing W and N together.

Fraction Formula: x = (A - B) / [10m × (10n - 1)]

How to Use This Calculator

  1. Choose whether the repeating decimal is positive or negative.
  2. Enter the whole part before the decimal point.
  3. Enter any digits that appear once after the decimal point.
  4. Enter the repeating block that continues forever.
  5. Choose how many preview digits you want to display.
  6. Press the convert button to see the result above the form.
  7. Review the raw fraction, simplified fraction, mixed number, ratio, and percent preview.
  8. Use the CSV or PDF buttons to save the result.

Example Data Table

Input Fraction Mixed Number Percent Preview
0.(3) 1/3 1/3 33.333333...
1.2(5) 113/90 1 23/90 125.555555...
2.41(6) 29/12 2 5/12 241.666666...
0.08(3) 1/12 1/12 8.333333...
3.(142857) 22/7 3 1/7 314.285714...

FAQs

1. What does this converter do?

It changes repeating decimals into exact fractions, mixed numbers, ratios, and percentage previews. It also shows the raw fraction before simplification and explains each solving step.

2. What is a repeating decimal?

A repeating decimal has one or more digits that continue forever in the same cycle. Examples include 0.(3), 1.2(5), and 3.(142857).

3. What are non-repeating digits?

These are digits that appear after the decimal point only once before the repeating cycle starts. In 2.41(6), the digits 41 are non-repeating.

4. Why does the calculator show a raw fraction?

The raw fraction displays the direct result from the formula before reduction. It helps students verify the algebraic setup and understand how simplification changes the numerator and denominator.

5. Can this handle negative values?

Yes. Choose the negative sign before converting. The calculator applies the sign to the final fraction, mixed number, decimal preview, ratio, and percentage preview.

6. Why are the results exact?

The converter uses digit-based fraction rules instead of rounded floating-point arithmetic. That makes the fraction exact for the repeating pattern you enter.

7. What does the Plotly graph show?

The graph separates the whole part, non-repeating part, and repeating contribution. It helps you see how each block builds the final decimal value.

8. When should I use more preview digits?

Use more preview digits when you want a longer decimal or percent display for checking homework, reports, or classroom examples. It does not change the exact fraction.

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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.