# Repeating decimal to fraction calculator

Decimal representation of a number is called repeating decimal, it is a number which keeps repeating itself after decimal. Use this online Repeating (recurring) decimal to fraction converter to convert recurring decimal to fraction.

## Recurring Decimal Calculator

Recurring or repeating decimals are continued numbers that do not terminate after the decimal point. The repeating decimal to fraction calculator handles all types of recurring decimal to fraction conversions at one click.

In this space, we will enlighten you about how repeating decimals to fractions calculator works, recurring decimal definition, and method to convert recurring decimal to fraction calculator with examples.

## How to use a recurring decimal calculator?

Follow these steps to use recurring decimals to fractions calculator** **for the conversion of non-terminating decimals.

- Enter the non-recurring part in the given input box.
- Enter a recurring number in the next input box.
- Hit the
**Calculate**button to get the fraction. - Use the
**Reset**button to enter new values.

In case, you need to convert a fraction to decimal, use our fraction to decimal calculator anytime.

## What is a recurring decimal?

As the name suggests, a recurring decimal is a value that keeps repeating itself after the decimal point. Wikipedia states that,

“A repeating decimal is the decimal representation of a number whose digits are repeating its values at regular intervals and the infinitely repeated portion is not zero.”

For example, if we solve the fraction ** 2/9,** we will get the repeating decimal as:

*0.222222….*

## How to convert repeating decimal to fraction?

Apart from using the repeating decimal calculator** **for decimal to fraction conversion, you should know the formal method to do so. We will also show you the repeating decimal to fraction trick** **in this method.

Follow these steps to perform the conversion by hand.

- Write down the value and assign it to a variable such as
or*x*to make it an equation*y**.* - Here’s the Multiply both sides of the equation by
if only*10*digit is repeating after the decimal point. Multiply by*1*if*100*digits are repeating and by*2*if*1000*digits are recurring.*3* - Subtract the equation acquired in 1
^{st}step from the equation in the 2^{nd} - Simplify the equation to get the fraction.

**Example:**

Find the fraction from the given recurring decimal?

*0.481481481….*

**Solution:**

**Step 1:** Assign the value to a variable.

*x**=**0.481481481…*

**Step 2:** Multiply the above equation by ** 1000** on both sides because there are

**digits repeating after the decimal.**

*3**1000x = 481.481481…*

**Step 3:** Subtract the equation acquired in **1 ^{st} step** from the equation in the

**2**

^{nd}step.*1000x – x = 481.481481 - 0.481481481*

**Step 4:** Simplify the equation to get the fraction.

*999x = 481*

*x = 481/999*

The GCF (greatest common factor) of **481** and **999** is ** 37.** Divide the numerator and denominator in the above fraction by

**to get the simplest value.**

*37**x = 13/27*

So, the repeating decimal ** 0.481481…** can be expressed as

**in fraction.**

*13/27*## Decimals to fractions chart

The following decimal to fractions table displays the values generated by our fraction to recurring decimal calculator**.**

0.41 recurring as a fraction | 41/99 | |

0.4 repeating as a fraction | 4/9 | |

0.52 repeating as a fraction | 52/99 | |

0.61 repeating as a fraction | 61/99 | |

0.29 recurring as a fraction | 29/99 | |

0.90 repeating as a fraction | 10/11 | |

0.06 recurring as a fraction | 2/33 | |

0.1 recurring as a fraction | 1/9 | |

0.05 recurring as a fraction | 5/99 | |

3.48 repeating as a fraction | 115/33 | |

0.53 repeating as a fraction | 53/99 | |

0.7 repeating as a fraction | 7/9 | |

0.95 repeating as a fraction | 95/99 | |

0.5 recurring as a fraction | 5/9 | |

0.41 repeating as a fraction | 41/99 | |

0.04 recurring as a fraction | 4/99 | |

0.004 recurring as a fraction | 4/999 | |

0.8 recurring as a fraction | 8/9 | |

0.7 recurring as a fraction | 7/9 | |

0.05 repeating as a fraction | 5/99 | |

0.04 repeating as a fraction | 4/99 | |

.3 repeating as a fraction | 1/3 | |

.6 repeating as a fraction | 2/3 |

### References:

- What is a Repeating Decimal? | Virtual Nerd.