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 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 decimalto 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.
- Input the integer number in the given box (Ex. 12, 45, 34 etc)
- Enter a recurring number in the next input box.
- Enter the non-recurring part (optional) in the given 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.
Example to use this repeating decimal to fraction calculator?
1. Let's suppose you want to enter 2.987777.
In this scenario you have,
- Integer: 2
- Recurring part: 7
- Non Recurring part: 98
2. Now, assume that you have to enter 0.4444.
In this situation you have,
- Integer: 0
- Recurring part: 4
- Non Recurring part: " ".
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,
“Arepeating decimal isthe decimal representationof a number whosedigitsarerepeating its values at regular intervals and theinfinitelyrepeated portion is notzero.”
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 to fractioncalculator for decimal to fraction conversion, you should know the formal method to do so. We will show you the repeatingdecimalto 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.
RepeatingDecimals to fractions chart
The following decimal to fractions table displays the values generated by ourrecurring decimal to fractioncalculator.
| 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 |
| 0.5recurringas 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.
