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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 x or y to make it an equation.
  • Here’s the Multiply both sides of the equation by 10 if only 1 digit is repeating after the decimal point. Multiply by 100 if 2 digits are repeating and by 1000 if 3 digits are recurring.
  • Subtract the equation acquired in 1st step from the equation in the 2nd
  • 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 3 digits repeating after the decimal.

1000x = 481.481481…

Step 3: Subtract the equation acquired in 1st step from the equation in the 2nd 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 37 to get the simplest value.

x = 13/27

So, the repeating decimal 0.481481… can be expressed as 13/27 in fraction.

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
0.52 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

References:

  1. What is a Repeating Decimal? | Virtual Nerd.