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.
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)]
| 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... |
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.
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).
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.
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.
Yes. Choose the negative sign before converting. The calculator applies the sign to the final fraction, mixed number, decimal preview, ratio, and percentage preview.
The converter uses digit-based fraction rules instead of rounded floating-point arithmetic. That makes the fraction exact for the repeating pattern you enter.
The graph separates the whole part, non-repeating part, and repeating contribution. It helps you see how each block builds the final decimal value.
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.
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.