Calculator
Enter a value like 0.(3), 0.1(6), or 2.58(3).
You can also use the separated fields.
Example Data Table
| Repeating Decimal | Non-Repeating Part | Repeating Part | Simplified Fraction | Mixed Number |
|---|---|---|---|---|
| 0.(3) | None | 3 | 1/3 | 1/3 |
| 0.1(6) | 1 | 6 | 1/6 | 1/6 |
| 2.58(3) | 58 | 3 | 31/12 | 2 7/12 |
| 12.45(09) | 45 | 09 | 3424/275 | 12 124/275 |
Formula Used
Let n be the count of non-repeating decimal digits.
Let r be the count of repeating digits.
For a decimal like W.A(B), use this method:
Fraction = (WAB - WA) / (10^n × (10^r - 1))
The denominator can also be written as r nines followed by n zeros.
Then reduce the fraction by the greatest common divisor.
How to Use This Calculator
- Enter the decimal in pattern form, such as
0.12(34). - Use separated fields when your keyboard does not support brackets.
- Add the whole number, non-repeating part, and repeating part.
- Select the output style you want.
- Press the convert button.
- Review the simplified fraction and calculation steps.
- Use CSV or PDF download for saving the result.
Repeating Decimal Conversion Guide
What a Repeating Decimal Means
A repeating decimal has one or more digits that continue forever. The repeated part is often shown with a bar. In this calculator, brackets show the same idea. For example, 0.(6) means 0.6666 forever. A value like 1.2(45) means 1.2454545 forever.
Why Fractions Are Better for Exact Work
Decimal forms can be easy to read. Yet repeating decimals are not complete on screen. A calculator may round them after a few places. Fractions keep the value exact. That is useful in algebra, finance, engineering, and exams. A simplified fraction also makes comparison easier.
How the Conversion Works
The method separates the fixed digits from the repeating digits. First, write all digits through one repeat cycle. Then subtract the digits before the repeat starts. The denominator uses nines and zeros. Nines match the repeating block. Zeros match the non-repeating block. The final fraction is reduced by the greatest common divisor.
Advanced Input Options
This tool accepts pattern input and separated input. Pattern input is faster for common values. Separated input is useful for careful checking. You can enter negative values too. You can also convert terminating decimals. If no repeating part is supplied, the tool treats the decimal as terminating.
Accuracy Tips
Use only the true repeating block. Do not add extra rounded digits. For 0.1666 forever, enter 0.1(6). Do not enter 0.1666 unless it stops there. Leading zeros inside a repeat are allowed. For example, 0.12(09) is valid. Always review the unsimplified fraction. It explains how the final answer was reduced.
FAQs
What is a repeating decimal?
A repeating decimal has digits that continue in the same pattern forever. Examples include 0.(3), 0.1(6), and 2.45(09).
How do I enter a repeating part?
Place the repeating digits inside brackets. For example, enter 0.12(34) when 34 repeats forever after 12.
Can this calculator handle negative decimals?
Yes. Use the negative sign selector or type a negative value in pattern form, such as -0.1(6).
What happens if I leave the repeat field empty?
The calculator treats the value as a terminating decimal. It still converts the decimal into a simplified fraction.
Why does the formula use nines?
Nines represent the repeating block. One repeating digit uses 9, two repeating digits use 99, and three use 999.
Why does the formula use zeros?
Zeros represent the non-repeating decimal places. Two fixed decimal digits require two zeros after the nines.
Can I download the result?
Yes. After conversion, use the CSV or PDF button above the form to download the displayed result.
Is the result simplified?
Yes. The calculator finds the greatest common divisor and reduces the fraction to its simplest form.